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Questions from the topic - 7. Discrete Fourier transform [7 hours] - Digital Signal Analysis and Processing
1. Why do we need Discrete Fourier Transform (DFT) although we have Discrete-time Fourier Transform (DTFT)? Find circular convolution between
x[n] = {1, 2} and y[n] = u[n] - u[n-4]. - 2070 Ashad
2. How fast is FFT? Draw the butterfly diagram and compute the value of x(7) using 8 pt DIT-FFT for the following sequences:
x(n) = {1, 0, 0, 0, 0, 0, 0, 0} - 2070 Ashad
3. Find $x_{3}[n]$ if DFT of $x_{3}[n]$ is given by $X_{3}(k) = X_{1}(k)X_{2}(k)$ where $X_{1}(k)$ and $X_{2}(k)$ are 4-point DFT of $x_{1}[n] = {1, 2, -2}$ and $x_{2}[n]$ = {1, 2, 3, -1} respectively. - 2069 Chaitra
4. Use the Fast Fourier Transform decimation in frequency algorithm to find the discrete Fourier Transform of the sequence x[n] = [1, -2, 2, 1]. - 2068 Bhadra
5. Find the FFT of the signal x[n] = (2, 1, 5, 3, 2, 1, 7). - 2065 Baisakh
6. Find the FFT of the signal x[n] = (3, 6, 5, 5, 3, 3, 6, 3). - 2065 Baisakh-Old