(Solved): Question 5 a) Find the DFT (Discrete Fourier Transform) of the series x[n]-(0.2,1,1,0.2), and sket ...

Question 5 a) Find the DFT (Discrete Fourier Transform) of the series x[n]-(0.2,1,1,0.2), and sketch the magnitude of the spectral components. Show all your calculations. [5 Marks] b) Use Matlab to find the DFT (Discrete Fourier Transform) of the series x[n] (0.2,1,1,0.2,1,1,0.2,1). If the samples were obtained at a sampling frequency of 1kHz, plot the actual magnitudes of the spectral components and the actual frequency spacing of the harmonics (bins). [5 Marks] c) You are to design a digital Low Pass filter to reduce the effects of high frequency noise. The digital low pass filter is to have a pass-band frequency range upto 1kHz. Due to limited computation power, and to prevent distortion, you decide to use a FIR filter with N=7 coefficients, and a sampling rate of T-200?s (F-5kHz). i) Use the Frequency Sampling method to calculate the FIR filter coefficients. ii) Sketch the structure of the filter using unit-delay elements. iii) Derive the difference equation of the filter. iv) Describe a simple method to transform your calculated filter coefficients to provide a high pass filter. What would the bandwidth of the resulting high pass filter be? [10 Marks] d) Describe the relative merits of using the Frequency Sampling and the 'Window' method for the design of digital FIR filters. [5 Marks] [End of Question 5] [End of Time Constrained Assessment]