Question

Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2 k-(N-1)/2 k-l You have designed a precision instrumentation system to capture data and post-process it. To reduce the effects of high frequency noise you are to implement a digital low pass filter with a pass-band range of 10kHz. Due to limited computation power, and to prevent distortion, you decide to use a FIR filter with N=5 coefficients, and updated at a sampling rate of T-20us (Fs-50kHz). i) Use the Frequency Sampling method to calculate the FIR filter coefficients i) Sketch the structure of the filter using unit-delay elements. ili) Derive the difference equation of the filter

Answer 1

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