Question

Filtering by masking DFT coefficients Consider the same chirp signal

from problem 2:
x[n]=cos(πn2/800),0≤n<400
Again, assume that x[n] was created by sampling a continuous-time chirp
signal x(t)= cos(5000πt2) at a rate fs=2000 Hz for a duration of 200 ms.

a. Using MATLAB or Python, find X[k]=DFT{x[n]}. Find the values of k
corresponding to frequencies between [−750 Hz,−250 Hz] and [250 Hz,750 Hz]

Answer 1

The question involves calculating the DFT of a chirp signal and finding the DFT coefficients that correspond to specific frequency ranges using MATLAB or Python.

Step-by-step explanation:

The student is asking to perform a Discrete Fourier Transform (DFT) on a sampled chirp signal using MATLAB or Python, and then to identify the values of k (frequency bins) that correspond to specific frequency ranges.

When dealing with a DFT, the frequency resolution is given by f_s / N, where f_s is the sampling frequency and N is the number of points in the DFT. Since the sampling frequency f_s is 2000 Hz and there are 400 samples, the frequency resolution is 5 Hz per bin. Therefore, to find the range between -750 Hz to -250 Hz and 250 Hz to 750 Hz, one would divide these frequency values by the resolution (5 Hz) to find the corresponding bin numbers (k values).

To calculate the DFT, one might use functions such as fft in MATLAB or Python's NumPy library. After computing the DFT, the specific values of k that correspond to the desired frequency range can be identified and analyzed.