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In this lab you will design and implement digital filters using a C program. Your programs will process WAV sound files. Software utilities are provided for testing your program to verify the proper frequency response. Prelab The PreLab addresses the definition and analysis of a moving average filter. The following statement defines the desired filter operation: “The output of the filter should be the average of the three most recent inputs.” a) Based on this specification, 1) Find the difference equation for this filter, i.e., y[n] = ... 2) Find the unit sample response (impulse response) h[n]. 3) Is this system FIR or IIR? 4) Find an analytical expression (equation) for the complex-valued Discrete-Time Fourier Transform (DTFT) Frequency Response of the system H(F); as well as the magnitude |H(F)|| and phase 2 H(F) response components. If you have not covered the Discrete-Time Fourier Transform in EE 328 yet, ...DON'T PANIC! This is simply the discrete-time version of the frequency response of the digital filter. If you have a non-recursive filter, the frequency response can be easily found from the difference equation: y[n] = Box[n] +Bıx[n-1] + B2x[n-2] + B3x[n-3] +... H(F) Bo + Bie-j27F + B2e-J47F + Bze-jóðF +... as: 5) Make a sketch of H(F) and Z H(F) versus digital frequency F. 6) Is the system high-pass, low-pass or bandpass? 7) Determine the half-power (or 3 dB) cutoff frequency of the filter, in terms of both the digital frequency Fc (cycles/sample) and the analog frequency fc (Hz). Assume a sampling rate S = 16 KHz.