- 1 Use Matlab Or Octave To Implement Discrete Convolution Discrete Fourier Transform Dft And Inverse Dft A Use Fun 1 (84.96 KiB) Viewed 56 times
assignment , this assignment reffer book is Signals analysis and
digital signal analysis,,,,plz solve this assignment ,,,,,i also
need.....plz early solved
1. Use Matlab or Octave to implement discrete convolution, discrete Fourier transform (DFT), and inverse DFT. a) Use functions conv() and fft() to verify the correctness of your implementation. b) Use function rand() to generate random signals of length 2^n, then compare the speed of your DFT implementation and fft(). Assume n is from 8 to 15. Plot the results. 2. Read the variable 'signal' from file 'computer_exercise.mat'. Assume this signal is sampled at 1000Hz, and contains noise. Answer the following questions. a) Compute the DFT of the signal. Use abs() to obtain the frequency spectrum's magnitude and use plot() to observe the result. Can you see any main frequency component, i.e., those frequencies with large magnitudes? If yes, what frequencies are they? b) If the observed main frequency components are useful part of the signal and others are considered as noise, compute the signal to noise ratio in dB using Parseval's theorem (signal to noise ratio is the ratio between signal power and noise power). c) If the signal's main frequency components can be identified, can you remove the noise and approximately restore the original signal? How?
3. Filtering the signal with a moving average filter. a) The impulse response of an N-point moving average filter is an N-point wide rectangular window with the height equal to 1/N. Filter the signal by convolving the signal with the filter's impulse response. Use N=3,5,7,9, 11. Plot and compare the signal before and after filtering. Is there any change in the waveform? b) Plot and observe the frequency response of the N-point moving average filter (i.e. DFT of the impulse response). If the highest frequency in the signal needs to be removed, what should be the value of N approximately? Validate the answer by filtering the signal with the chosen N-point moving average filter and observing the result's spectrum. Tips: 1) Functions tic() and toc() can be used for speed testing. To increase accuracy, you can repeat the same experiment many times and take the average time. 2) Function plot() can be used for plotting curves.