Electrocardiogram enhancement system and method

Claims

We claim:

1. A method for enhancing an electrocardiogram signal having frequency, low amplitude notches that are difficult to visually detect within an electrocardiogram signal waveform and that have frequencies above the signal recording bandwidth of a conventional chart recorder, said signal having a plurality of frequency components, each frequency component having a frequency, phase and amplitude, the frequencies of the frequency components comprising a first inter-component frequency relationship and the phases of the frequency components comprising a first inter-component phase relationship said enhancement method comprising the steps of:

selectively amplifying frequency components representing the notches relative to other frequency components in the electrocardiogram signal; and

expanding said electrocardiogram signal including the amplified frequency components in time scale by a time scale expansion factor, frequency components representing said expanded signal having a second intercomponent frequency relationship and a second inter-component phase relationship equivalent to said first inter-component frequency relationship and first inter-component phase relationship, said expanded signal having a frequency range within the bandwidth of a conventional chart recorder.

2. The method of claim 1 wherein said expanding of said electrocardiogram signal in the time scale comprises dividing the frequency of each frequency component by a time scale expansion factor.

3. The method of claim 2 wherein said time scale expansion factor is greater than one.

4. The method of claim 1 wherein said selectively amplifying said electrocardiogram signal comprises:

selecting those frequency components of the electrocardiogram signal within a predetermined frequency range and greater than a minimum amplitude value indicative of notches; and

multiplying each of the selected frequency components by an amplification factor.

5. The method of claim 4 wherein said frequency range is greater than 100 up to and including 1200 Hz.

6. The method of claim 4 wherein said minimum amplitude value is determined to exclude high frequency signal noise.

7. The method of claim 6 wherein said minimum amplitude value is greater than 5% of the peak amplitude of notch frequency components.

8. The method of claim 4 wherein the amplification factor is equal to the ratio of a peak amplitude of non-notch frequency components to a peak amplitude of the notch frequency components multiplied by a gain factor.

9. The method of claim 8 where the gain factor ranges from a value greater than zero up to one.

10. The method of claim 1 further comprising:

generating a Fourier transform of the electrocardiogram signal to obtain a frequency spectrum comprising the frequency components representing the electrocardiogram signal; and

generating an inverse Fourier transform of the frequency spectrum after selectively amplifying and expanding the frequency component of the signal.

11. The method of claim 1 further comprising the step of accurately recording the expanded signal and displaying the high frequency, low amplitude notches.

12. A method for enhancing an electrocardiogram signal in a first frequency range having high frequency, low amplitude notches that are difficult to visually detect and analyze within an electrocardiogram signal waveform and that have frequencies above the signal recording bandwidth of a conventional chart recorder, said enhancement method comprising the steps of:

performing a Fourier transform operation upon the electrocardiogram signal whereby a frequency spectrum signal is obtained, said frequency spectrum signal comprising frequency components having an amplitude, frequency, and phase, the frequencies of the frequency components comprising a first inter-component frequency relationship and the phases of the frequency components comprising a first inter-component phase relationship;

selecting frequency components within a predetermined frequency range and greater than a minimum amplitude value that are indicative of notches;

amplifying each of the selected frequency components by an amplification factor;

expanding the frequency spectrum signal in time scale by dividing each frequency component by a time scale expansion factor, frequency components having a second inter-component frequency and second inter-component phase relationship equivalent to said first inter-component frequency and first inter-component phase relationship; and

performing an inverse Fourier transform operation upon the expanded frequency spectrum signal to obtain an enhanced electrocardiogram signal, said enhanced electrocardiogram signal having a frequency range within the signal recording bandwidth of conventional chart recorders.

13. The method of claim 12 wherein said time scale expansion factor is greater than one.

14. The method of claim 12 wherein said amplification factor is a value equal to the ratio of a peak amplitude of non-notch frequency components to a peak amplitude of the notch frequency components multiplied by a gain factor.

15. The method of claim 14 wherein said gain factor ranges from a value greater than zero up to one.

16. The method of claim 12 wherein said frequency range is greater than 100 up to and including 1200 Hz.

17. The method of claim 12 wherein said minimum amplitude value is determined to exclude high frequency signal noise.

18. The method of claim 17 wherein said minimum amplitude value is greater than 5% of the peak value of the notch frequency components.

19. The method of claim 12 further comprising the step of accurately recording the enhanced electrocardiogram waveform and displaying the high frequency, low amplitude notches.

20. Apparatus for enhancing an electrocardiogram signal having high frequency, low amplitude notches that are difficult to visually detect within an electrocardiogram signal waveform and that have frequencies above the signal recording bandwidth of a conventional chart recorder, said signal having a plurality of frequency components, each frequency component having a frequency, phase and amplitude, the frequencies of the frequency components comprising a first inter-component frequency relationship and the phases of the frequency components comprising a first inter-component phase relationship, said apparatus comprising:

means for selectively amplifying frequency components representing the notches relative to other frequency components in the electrocardiogram signal; and

means for expanding said electrocardiogram signal including the amplified frequency components in time scale by a time scale expansion factor, frequency components representing said expanded signal having a second inter-component frequency relationship and second inter-component phase relationship equivalent to said first inter-component frequency relationship and first inter-component phase relationship, said expanded signal being within the bandwidth of a conventional chart recorder, whereby the expanded signal is accurately recorded, and the high frequency, low amplitude notches are made visible

21. The apparatus of claim 20 wherein the means for expanding said electrocardiogram signal in the time scale comprises a means for dividing the frequency of each frequency component by a time scale expansion factor.

22. The apparatus of claim 21 wherein said time scale expansion factor is greater than one.

23. The apparatus of claim 20 wherein the means for selectively amplifying said electrocardiogram signal comprises:

means for selecting frequency components within a predetermined frequency range and greater than a minimum amplitude value indicative of notches; and

means for amplifying each of the selected frequency components by an amplification factor.

24. The apparatus of claim 23 wherein said frequency range is greater than 100 up to and including 1200 Hz.

25. The apparatus of claim 23 wherein said amplitude range excludes high frequency signal noise.

26. The apparatus of claim 25 wherein said minimum amplitude value is equal to 5% of the peak value of the notch frequency components.

27. The apparatus of claim 23 wherein said amplification factor is equal to the ratio of a peak amplitude of non-notch frequency components to a peak amplitude of the notch frequency components multiplied by a gain factor.

28. The apparatus of claim 27 wherein said gain factor ranges from a value greater than zero up to one.

29. The apparatus of claim 20 further comprising:

means for generating a Fourier transform of the electrocardiogram signal to obtain a frequency spectrum comprising the frequency components representing the electrocardiogram signal; and

means for generating an inverse Fourier transform of the frequency spectrum after selectively amplifying and expanding in the time scale the frequency components of the signal.

30. The apparatus of claim 29 wherein the means for generating a Fourier transform, means for selectively amplifying, means for expanding and means for generating an inverse Fourier transform comprises a microprocessor.

31. The apparatus of claim 20 further comprising a means for counting the high frequency notches and a means for displaying said count of notches.

32. The apparatus of claim 31 wherein the means for counting the notches comprises:

means for detecting the beginning and end of a QRS wave of the electrocardiogram signal waveform;

means for calculating the slope of the waveform at a first test point;

means for calculating the slope of the waveform at a second subsequent test point, said second test point being a predetermined time period after said first test point;

means for comparing the slopes of said first and second test points;

means for incrementing a notch counter if the signs of said slopes of said test points are not equal;

means for setting said first test point equal to said second test point wherein the means for calculating the slope of the waveform at the second test point, means for comparing the slopes of said first and second test points and means for incrementing said notch counter continue to operate to sequence until the end of the QRS wave is detected.

33. The apparatus of claim 31 wherein the means for counting the notches comprises:

a threshold detector which generates an output pulse upon detection of those notches of a predetermined minimum amplitude;

means for inputting selected frequency components indicative of notches to the threshold detector; and

a digital counter which counts the output pulses of the threshold detector.

34. The apparatus of claim 20 further comprising a chart recording device for the display of said expanded signal whereby the electrocardiogram signal is accurately recorded and the high frequency, low amplitude notches are visible in the displayed signal.

35. The apparatus of claim 20 further comprising means for accurately recording the expanded signal and means for displaying the high frequency, low amplitude notches.

36. Apparatus for enhancing an electrocardiogram signal in a first frequency range having high frequency, low amplitude notches that are difficult to visually detect and analyze within a electrocardiogram signal waveform and that have frequencies above the signal recording bandwidth of a conventional chart recorder comprising:

means for performing a Fourier transform operation upon the electrocardiogram signal whereby a frequency spectrum signal is obtained, said frequency spectrum signal comprising frequency components having an amplitude, frequency, and phase, the frequencies of the frequency components comprising a first inter-component frequency relationship and the phases of the frequency components comprising a first inter-component phase relationship;

means for selecting frequency components within a predetermined frequency range and greater than a minimum amplitude value that are indicative of notches;

means for amplifying each of the selected frequency components by an amplification factor;

means for expanding the frequency spectrum in time scale by dividing each frequency component by a time scale expansion factor, frequency components having a second inter-component frequency relationship and a second inter-component phase relationship equivalent to said first inter-component frequency relationship and first inter-component phase relationship;

means for performing an inverse Fourier transform operation upon the expanded frequency spectrum signal to obtain an enhanced electrocardiogram signal, said enhanced electrocardiogram signal having a frequency range within the bandwidth of conventional chart recorders; and

chart recording means for display of the expanded signal where in the high frequency, low amplitude notches are visible within the displayed signal.

37. The apparatus of claim 36 wherein the means for performing a Fourier transform, means for selecting frequency components, means for amplifying the selected frequency components, means for expanding the frequency spectrum and means for performing an inverse Fourier transform comprises a microprocessor.

38. The apparatus of claim 36 wherein said time scale expansion factor is greater than one.

39. The apparatus of claim 36 wherein said amplification factor is equal to the ratio of a peak amplitude of non-notch frequency components to a peak amplitude of the notch frequency components multiplied by a gain factor.

40. The apparatus of claim 39 wherein said gain factor ranges from a value greater than zero up to one.

41. The apparatus of claim 36 wherein said frequency range is greater than 100 up to and including 1200 Hz.

42. The apparatus of claim 36 wherein said minimum amplitude value excludes high frequency signal noise.

43. The apparatus of claim 42 wherein said minimum amplitude value is 5% of the peak value of the notch frequency components.

44. A method for enhancing an electrocardiogram signal having high frequency, low amplitude notches that have frequencies above 100 Hz and are difficult to visually detect within an electrocardiogram signal waveform, said signal having a plurality of frequency components, each frequency component having a frequency, phase and amplitude, said enhancement method comprising the steps of:

amplifying the frequency components above 100 Hz relative to other frequency components in the electrocardiogram signal by an amplification factor; and then

expanding said electrocardiogram signal including the amplified frequency components in time scale by a time scale expansion factor to produce an expanded signal, said expanded signal having frequency components in which the frequencies are those of the frequency components of the electrocardiogram signal divided by the time scale expansion factor, said expanded signal having a frequency range within the bandwidth of a conventional chart recorder.

45. The method for enhancing an electrocardiogram signal of claim 44 wherein said frequencies of the frequency components of the electrocardiogram signal comprise a first inter-component relationship and the phases of the frequency components comprise a first inter-component phase relationship and frequencies of the frequency components of the expanded signal comprise a second inter-component frequency relationship equivalent to said first inter-component frequency relationship and the phases of the frequency components comprise a second inter-component phase relationship equivalent to said first inter-component phase relationship.

46. The method for enhancing an electrocardiogram signal of claim 44 further comprising:

generating a Fourier transform of the electrocardiogram signal to obtain a frequency spectrum comprising the frequency components representing the electrocardiogram signal; and

generating an inverse Fourier transform of the frequency spectrum after amplifying and expanding the signal.

47. The method of claim 44 further comprising displaying the high frequency, low amplitude notches.

48. Apparatus for enhancing an electrocardiogram signal having high frequency, low amplitude notches that have frequencies above 100 Hz and are above the signal recording bandwidth of a conventional chart recorder and difficult to visually detect within an electrocardiogram signal waveform, said signal being within a first frequency range and having a plurality of frequency components, each frequency component having a frequency, phase and amplitude, said apparatus comprising:

means for amplifying the frequency components above 100 Hz relative to other frequency components in the electrocardiogram signal by an amplification factor; and

means for expanding said electrocardiogram signal including the amplified frequency components in time scale by a time scale expansion factor to produce an expanded signal, said expanded signal having frequency components in which the frequencies are those of the frequency components of the electrocardiogram signal divided by the time scale expansion factor, said expanded signal having a frequency range within the bandwidth of a conventional chart recorder.

49. The apparatus of claim 48 wherein said frequencies of the frequency components of the electrocardiogram signal comprise a first inter-component frequency relationship and the phases of the frequency components comprise a first inter-component phase relationship and frequencies of the frequency components of the expanded signal comprise a second inter-component frequency relationship equivalent to said first inter-component frequency relationship and the phases oaf the frequency components comprise a second inter-component phase relationship equivalent to said first inter-component phase relationship.

50. The apparatus of claim 48 further comprising:

means for generating a Fourier transform of the electrocardiogram signal to obtain a frequency spectrum comprising frequency components representing the electrocardiogram signal; and

means for generating an inverse Fourier transform of the frequency spectrum after amplifying and expanding the signal.

51. The apparatus of claim 48 further comprising a chart recording device for the display of said expanded signal whereby the electrocardiogram signal is accurately recorded and the high frequency, low amplitude notches are visible in the displayed signal.

52. The apparatus of claim 48 further comprising means for displaying the high frequency, low amplitude notches.

FIELD OF INVENTION

The system of the present invention relates to the enhancement of electrocardiogram signals. Particularly the system relates to the enhancement of small amplitude, high frequency notches and slurs which are difficult to record on conventional chart recorders and difficult to visually detect within an electrocardiogram waveform by medical personnel.

BACKGROUND OF THE INVENTION

An electrocardiograph records electric potentials generated by the neuromuscular mechanism of the heart. A stimulus arising in the sino-auricular node of the heart sets up a tiny electric current called the excitation or depolarization wave. This wave spreads over the auricular wall and the auricles contract. When the excitation wave is at the junctional tissue between auricle and ventricle, it is delayed by the atrioventricular node at the beginning of the Bundle-of-His. The excitation wave conducts rapidly through the Bundle and then branches to the left and right ventricle.

The excitation wave then conducts slowly through the Purkinje fibers which terminate in the ventricular muscle, causing the ventricles to contract. A period of heart rest follows, after which a fresh impulse arises at the sino-aurircular node and the contraction- cycle once again repeats. By placing electrodes on the chest of a patient, a time varying voltage corresponding to the spreading excitation wave can be measured.

This excitation waveform, referred to as an electrocardiogram (ECG), is used to analyze the operation of the heart. The electrocardiogram is divided up into five time segments, known to those skilled in the art as, P, Q, R, S, and T which correspond to the different parts of the waveform. The "P" or Auricular Wave corresponds to the spread of the wave through the auricular musculature. At the point the wave spreads over the ventricular neural net of the Bundle-of-His, a rapid rise and fall of the wave potential, referred to as the "R" wave occurs. Before the "R" wave portion, a small dip called the "Q" wave occurs in the electrocardiogram while after the "R" wave a large drop in the electrocardiogram occurs called the "S" wave. The final portion of the electrocardiogram, the "T" wave, corresponds to the resting phase of the ventricle during which time an electrical repolarization of the ventricular muscle occurs. After the "T" wave the electrocardiogram reflects a horizontal line or isoelectric baseline indicating a period of heart rest prior to the next cycle of the excitation wave.

By analyzing deviations in the shape of the electrocardiogram, physicians can diagnose pathological conditions which relate to the heart and circulatory system. Typically the electrocardiogram is recorded by a paper chart recorder and examined for deviations in the shape of the various segments of the waveform.

Most chart recorders can accurately record waveforms occurring at frequencies up to 100 Hz. However, waveforms occurring at frequencies greater than 100 Hz are outside the bandwidth of the chart recorder and are distorted or lost when recorded since the changes in the waveform occur too rapidly for the pen or stylus of the chart recorder to follow. For example, conventional ECG chart recorders cannot display the small rapid variations in the waveforms, having frequencies typically in the range of 600 to 1000 Hz, referred to as notches and slurs (hereinafter referred to as "notches") which are common to the QRS complex of patients with clinical and preclinical heart disease.

In one method to overcome the limited bandwidth of an ECG chart recorder, ECG signals are routed for display to a cathode-ray tube. The display generated is then photographed to produce a permanent recording of the waveform. This method is used in research facilities as a research tool and is not readily accessible to cardiologists, internists, and general practitioners outside this environment.

U.S. Pat. No. 4,565,201 describes a signal averaging means which includes a microcomputer programmed to output information indicative of the ECG signal at a fraction of the speed of which it was input to the microcomputer. However, since the notches are small and difficult to detect, cardiologists, internists and other medical personnel cannot detect and analyze the notches with any degree of confidence.

One method to overcome the problem of visual detection and analysis of the notches is to amplify the signal. However since the amplitude of the notches is extremely small, (the ratio of the maximum amplitude of a ECG waveform to the maximum amplitude of a notch may be from 1:50 to 1:20) amplification of the entire waveform to increase the visibility of the notches would drive the signal off scale, saturating the display/recording device. Thus when the signal is amplified to display the notches, the entire ECG waveform cannot be recorded by the chart recorder. In addition, since the notches occur quite frequently near the minimum and maximum amplitudes of the waveform, simultaneous recording of all the notches at the desired amplification is extremely difficult. It has been found that it is preferable that not only the notches, but the entire waveform and the positions of the notches with respect to the waveform be displayed/recorded for proper analysis and diagnosis.

U.S. Pat. No. 3,809,071 describes a means to amplify and display low level signals without saturating the display/recording device. However in this method the larger amplitude signals which are amplified off the scale of the display/recording device are simply cut off at the point of saturation Thus only the small amplitude signals are accurately displayed/recorded.

It is an object of the present invention to provide a means for enhancing electrocardiogram signals such that the waveform may be accurately recorded on a conventional chart recorder.

It is an object of the present invention to provide a means for enhancing electrocardiogram signals in a manner that medical personnel can easily detect and analyze small amplitude, high frequency notches often found in patients with clinical heart disease.

It is an object of the present invention to provide an automatic electrocardiogram enhancement system which is simple for medical personnel to use.

SUMMARY OF THE INVENTION

In the ECG enhancement system of the present invention, small amplitude, high frequency notches associated with myocardial disease and arrhythmias can be recorded by conventional chart recorders. In addition, the notches are clearly visible in the recorded waveform for easy visual detection, inspection and analysis by medical personnel.

In the system of the present invention, ECG signals having small amplitude, high frequency notches are automatically enhanced, first, by selectively amplifying the notches while keeping the amplitude of the remainder of the waveform constant and second, by uniformly expanding the signal in the time domain wherein the inter-component frequency and inter-component phase relationships of the signal are maintained Because the enhancement system of the present invention automatically adjusts the enhancement parameters, the system is simplified and easy to use by medical personnel.

In one embodiment of the present invention, a Fast Fourier Transform (FFT) is performed on the input signal to derive the frequency spectrum of the ECG signals. The frequency components of the spectrum representing the notches are amplified and the entire frequency spectrum is translated into a lower frequency range. The enhanced signal is subsequently transformed back into a time varying signal.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects, features and advantages of the present invention will be apparent from the following detailed description of a preferred embodiment of the invention in which:

FIG. 1 is an illustration of the time varying waveform that comprises an electrocardiogram.

FIG. 2 displays an electrocardiogram where high frequency notches are present.

FIG. 3(a) illustrates an unaltered time varying electrocardiogram signal as would be displayed on an Electrocardiograph chart recorder.

FIG. 3(b) shows the same electrocardiogram signal in which the frequency components representing the notches have been amplified relative to the rest of the signal.

FIG. 3(c) shows the electrocardiogram signal uniformly "expanded" in the time scale.

FIG. 4(a) illustrates the unaltered electrocardiogram signal in the frequency domain.

FIG. 4(b) shows the same signal after the amplitudes of the frequency components representing the notches have been amplified.

FIG. 4(c) shows the signal after time scale expansion.

FIG. 5 is a block diagram of an embodiment of the ECG enhancement system of the present invention.

FIGS. 6(a) and 6(b) is a flow diagram illustrating an embodiment of the electrocardiogram enhancement system of the present invention.

FIG. 7 is a block diagram of an apparatus for detecting and counting notches in the electrocardiogram waveform.

FIG. 8 is a flow diagram for a method of detecting and counting notches in the electrocardiogram waveform.

DETAILED DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the waveform of an electrocardiogram which comprises waveform segments "P" 10, "Q" 20, "R" 30, "S" 40, and "T" 50. FIG. 2 shows the high frequency notches 60 that are common in the QRS complex in the case of coronary artery disease. These notches are characterized by small amplitude, rapid time variations that cannot be accurately reproduced by conventional chart recorders.

In order for the ECG waveform to be useful for diagnostic analysis, the high frequency notches must be clearly visible within the waveform so that they can be inspected and analyzed by medical personnel. It is also necessary that the waveform be uniformly translated or expanded in the time domain, to a frequency range within the bandwidth of the chart recorder, in order that the original shape of the waveform (except for the amplified notches) can be accurately recorded on the chart recorder. In other words, each frequency and phase component of the waveform must be consistently modified in order to produce a translated waveform having a frequency range within the bandwidth of the chart recorder, in which the signal component amplitudes, inter-component frequency relationships and inter-component phase relationships among the integral signal components are maintained.

Through the ECG enhancement system of the invention the original signal, as illustrated in FIG. 3a, is automatically enhanced, first by selectively amplifying the notches 60 without affecting the rest of the waveform, as illustrated in FIG. 3b and, second, by uniformly expanding in the time domain the entire signal, as illustrated in FIG. 3c, in a manner that the high frequency notches 60 can be accurately reproduced by a chart recorder while maintaining the shape of the waveform.

In the present invention, the frequency spectrum of an ECG signal is approximated by calculating the discrete Fourier Transforms (DFT) of the waveform. This is accomplished by an algorithm generally known as a Fast Fourier Transform (FFT) which rapidly makes the computations required to obtain the DFT of an input signal. As a result of the FFT calculations, the frequency spectrum of the input waveform signal is approximated by a series of points or frequency components at different discrete frequencies having amplitudes which correspond to the amplitudes of the input waveform signal at the respective discrete frequencies. Since a set of points defined by discrete frequency, amplitude and phase values result from performing the FFT operation, the sampled frequency spectrum signal obtained using the FFT operation is easily manipulated by performing mathematical operations on these values as discussed in detail below.

The notches which occur in the ECG waveform are very difficult to visually detect and analyze. Therefore it is desirable that these notches be selectively amplified with respect to the remainder of the waveform. In other words selective amplification permits only the notches to be amplified; the remainder of the waveform is not affected. The amplitude of each frequency component with a predetermined frequency range and greater than a minimum amplitude value indicative of notches is multiplied by an amplification factor "H". The value of "H" is selected such that the amplification of the notches is sufficient for visual detection and analysis of the notches, but not too large that the recording device is saturated, that is, the limits of the device are not exceeded. Preferably the value of H is determined by calculating the ratio of the largest amplitude of the frequency components representing the ECG signal, i.e. the "non-notch" frequency components, to the largest amplitude of the frequency components representing the notches, i.e. the notch frequency components, and multiplying the ratio by a gain factor "G" such that the notch is easily discernible without significantly changing the shape of the wave. More particularly, the value of H is determined by calculating the ratio of the largest amplitude of those frequency components up to and including 100 Hz to the largest amplitude of those frequency components greater than 100 Hz and multiplying the ratio by the gain factor G. The gain factor G may be determined empirically based on the waveform. Preferably G ranges from a value greater than zero up to one. Most preferably G is equal to 1/4.

The frequency range and minimum amplitude value are set such that only the frequency components representing the high frequency notches are amplified. The frequency components representing a notch typically center around frequencies in the range of 600-1000 Hz, while the frequency components representing the remainder of the waveform are below 100 Hz. However, it has been found that the spectrum of frequency components representing a notch may range from 100 to 1500 Hz. Although the frequency components representing a notch may range from 100 to 1500 Hz, it is preferred that the frequency range is greater than 100 Hz up to and including 1200 Hz, thereby accounting for the majority of notch frequency components. The minimum amplitude is selected to exclude high frequency signal noise which can distort the signal. Preferably the minimum amplitude is approximately 5% of the peak amplitude of the notch frequency components, that is, the frequency components above 100 Hz.

Once the frequency components representing the notches are amplified, the frequency spectrum representing the entire waveform is translated to a lower frequency range that is within the bandwidth of the chart recorder. The frequency components are translated or shifted down by dividing the frequency of each of the frequency components by a time scale expansion factor, K. This time scale expansion factor is chosen so that the higher frequency components are translated down to lower frequencies within the bandwidth of the chart recorder while other lower frequency components that are also translated remain within the bandwidth of the chart recorder. The time scale expansion factor may be preselected or, alternatively, may be calculated based upon the highest frequency component detected. For example, if the bandwidth of the chart recorder is 100 Hz and the highest frequency component is 1000 Hz then K=1000/100=10.

The translated frequency spectrum is subsequently transformed back into a time varying signal by performing an inverse FFT operation. Since the FFT components comprise both real and imaginary elements, thus taking into account both the frequency and phase elements of the signal, the operation of translating the frequency spectrum does not alter the inter-component phase and inter-component frequency relationships among the components in the spectrum. Therefore, except for the deliberate amplification of the notches, the expanded waveform in the time domain maintains its original shape.

Referring to FIGS. 4a and 4b, the frequency components in the range greater than 100 Hz up to and including 1200 Hz represent notches. Illustratively, A.sub., the peak value of the non-notch frequency components, and A.sub.2, the peak value of the notch frequency components have values of 200 mv and 10 mv respectively. Therefore the amplification factor is H=A.sub.1 /A.sub.2 .times.G=200/10.times.1/4=5. Thus the frequency components representing the notches in FIG. 4a are increased in amplitude by a factor of 5, as shown in FIG. 4b. The frequency components 100 Hz and below, which represent the remainder of the signal, have not been altered.

The frequency spectrum illustrated in FIGS. 4b is then translated or expanded in the time scale by a factor of 10 as illustrated in FIG. 4c. As can be seen by comparing FIGS. 4b and 4c, the 1000 Hz frequency component in FIG. 4b has been translated so that it is now at 100 Hz in FIG. 4c. Similarly, the frequencies of the remaining components in the signal shown in FIG. 4b are all divided by the time scale expansion factor resulting in the frequency spectrum illustrated in FIG. 4c. Although the time scale expansion factor K used to obtain the frequency spectrum of FIG. 4c from that shown in FIG. 4b is equal to 10, this value for K is only used as an example and other values for K can be used.

The inter-component phase and inter-component frequency relationships remain equivalent. As shown in FIG. 4b, the 50 Hz and 100 Hz components are separated by one octave. In FIG. 4c, the respective translated frequency components, at 5 Hz and 10 Hz, are also separated by one octave. Thus, the inter-component frequency and inter-component phase relationships in the signal are maintained in the enhanced signal after the entire frequency spectrum of the signal is translated into a range suitable for accurate reproduction of the signa