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x(t) Doppler ultrasound signals used for measuring blood flow are often complex, and Fourier analysis helps in breaking them down into their frequency components. This is essential for understanding the speed and direction of blood flow. 3 2 1 -1 -2 -3 -3 -2 -1 0 1 2 3 t(s) (a) (40 points) Calculate the Fourier series for the signal shown above, which approximately represents a Doppler ultrasound signal reflected from moving blood cells. (b) (10 points) Using Matlab, calculate the first five terms (up to n or k = 5) and plot it along with the original signal (use a sampling frequency of fs = 1 kHz). (c) (10 points) Write down the expressions for the polar form of the Fourier series using results from part (a) (i.e. calculate Ck and 0k). Use Matlab to calculate the first five terms (up to n or k = 5) of the polar form, plot it, and compare it with the rectangular (Cartesian) form you obtained in part (b). (d) (10 points) Plot the triangular wave in the frequency domain (plot |C| vs. frequency). Use stem function for the plot.

x(t) Doppler ultrasound signals used for measuring blood flow are often complex, and Fourier analysis helps in breaking them down into their frequency components. This is essential for understanding the speed and direction of blood flow. 3 2 1 -1 -2 -3 -3 -2 -1 0 1 2 3 t(s) (a) (40 points) Calculate the Fourier series for the signal shown above, which approximately represents a Doppler ultrasound signal reflected from moving blood cells. (b) (10 points) Using Matlab, calculate the first five terms (up to n or k = 5) and plot it along with the original signal (use a sampling frequency of fs = 1 kHz). (c) (10 points) Write down the expressions for the polar form of the Fourier series using results from part (a) (i.e. calculate Ck and 0k). Use Matlab to calculate the first five terms (up to n or k = 5) of the polar form, plot it, and compare it with the rectangular (Cartesian) form you obtained in part (b). (d) (10 points) Plot the triangular wave in the frequency domain (plot |C| vs. frequency). Use stem function for the plot.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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x(t) Doppler ultrasound signals used for measuring blood flow are often complex, and Fourier analysis helps in breaking them down into their frequency components. This is essential for understanding the speed and direction of blood flow. 3 2 1 -1 -2 -3 -3 -2 -1 0 1 2 3 t(s) (a) (40 points) Calculate the Fourier series for the signal shown above, which approximately represents a Doppler ultrasound signal reflected from moving blood cells. (b) (10 points) Using Matlab, calculate the first five terms (up to n or k = 5) and plot it along with the original signal (use a sampling frequency of fs = 1 kHz). (c) (10 points) Write down the expressions for the polar form of the Fourier series using results from part (a) (i.e. calculate Ck and 0k). Use Matlab to calculate the first five terms (up to n or k = 5) of the polar form, plot it, and compare it with the rectangular (Cartesian) form you obtained in part (b). (d) (10 points) Plot the triangular wave in the frequency domain (plot |C| vs. frequency). Use stem function for the plot.
Transcribed Image Text:x(t) Doppler ultrasound signals used for measuring blood flow are often complex, and Fourier analysis helps in breaking them down into their frequency components. This is essential for understanding the speed and direction of blood flow. 3 2 1 -1 -2 -3 -3 -2 -1 0 1 2 3 t(s) (a) (40 points) Calculate the Fourier series for the signal shown above, which approximately represents a Doppler ultrasound signal reflected from moving blood cells. (b) (10 points) Using Matlab, calculate the first five terms (up to n or k = 5) and plot it along with the original signal (use a sampling frequency of fs = 1 kHz). (c) (10 points) Write down the expressions for the polar form of the Fourier series using results from part (a) (i.e. calculate Ck and 0k). Use Matlab to calculate the first five terms (up to n or k = 5) of the polar form, plot it, and compare it with the rectangular (Cartesian) form you obtained in part (b). (d) (10 points) Plot the triangular wave in the frequency domain (plot |C| vs. frequency). Use stem function for the plot.
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