Homework #5: Application of Spectrogram – Spectral Doppler

In this homework, you will practice applying spectrogram to form an ultrasound
Spectral Doppler image”.
Basically, the spectral Doppler in biomedical ultrasound is to perform time-frequency
analysis (e.g., short time DFT or spectrogram, see Eq. (7.203) in the textbook) over
the acquired Doppler data set. Below is a representative screen shot of Spectral
Doppler.
Spectral Doppler
Time
Frequency
(i.e., Doppler shift)
Velocity
Time
Velocity (from Doppler frequency shift)
+ _
Positive shift
Negative shift
(a) Please implement your own DFT function myDFT() and DFT shift function
myDFTshift(). You may verify your myDFT() and myDFTshift() by MATLAB
built in function fft() and fftshift(). Use myDFT() and my DFTshift() to verify
the effect of time windowing – comparing rectangular and Bartlett windows
given your own provided signals. Note that zero-padding on your own
provided signals before you performs DFT are required. Note that you have to
take care the sequence between zero-padding and windowing and comments
the results obtained from the difference sequences. To speed up myDFT()
execution, you may try to implement it in the matrix form.
(b) Given the Doppler data set, SpectralDopplerData.mat, write your own
spectrogram function – myspectrogram() from scratch (see Fig. 7.34) to
implement spectral Doppler as indicated in the above figure, i.e.,
time-frequency analysis over the provided Doppler data set. Note that You
have to use the myDFT() and myDFTshift() developed in (a) in your2/3
myspectrogram(), and have to show the Spectral Doppler with correct axes
(see the above figure).
Note that
- Your own spectrogram function should have the following function
definition.
[S, F, t] = myspectrogram(x, window, Noverlap, Nfft, Fs)
The input/output of this function resembles the MATLAB function
spectrogram(). Generally, Nfft is larger than (i.e., zero padding is performed)
or equal to the length of window. Please “doc” spectrogram() to see the
details of input/output parameters.
- You can convert the frequency (Doppler frequency shift) to velocity by v =
FDoppler*lambda/2, where FDoppler: Doppler shift and lambda: wavelength of
the applied ultrasound
- Here the positive or negative sign of frequency, i.e., FDoppler, has its physical
meaning, representing the direction of velocity; therefore, you have to
show positive and negative frequency parts (i.e., positive and negative
velocities) simultaneously.
- Nfft: not smaller than 64
- After load(‘SpectralDopplerData.mat’), there are three variables –
DopplerData, PRF (pulse repetition frequency, in Hz, which is equivalent
to Fs), and lambda (ultrasound wavelength, in meter)
(c) Adjust the window length, window type (Hann, Hamming, Rectangular, or
else. See also MATLAB functions – window(), hann(), hanning() and
hamming()), and overlapping ratio (i.e., Noverlap/window length*100%) to
see how the spectral Doppler changes. Describe and justify what you observe.
To simplify your comparison, remember to fix the other parameters while
adjusting one certain parameter (explained in the class).
(d) Write a function to implement audio Doppler, that is, playing the Spectral
Doppler by two-channel stereo audio. In audio Doppler, we send the signals
representing the part of positive frequency to left channel and those
representing the part of negative frequency to right channel. Details please
find in the following figure. Please describe how your implement audio
Doppler, and remember to hand in the audio Doppler as a wave (*.wav) file.
Can you figure out or hear anything from the difference between left channel
and right channel in audio Doppler?3/3