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EL 6183 Week No 4

# EL 6183 Week No 4 - Polytechnic University EL 6183 EE 4163...

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Polytechnic University EL 6183 EE 4163 DSP lab Lab #4 FIR Filter: Design and Implementation A) At the end of this lab, students will be able to: Design Low Pass, High Pass, Band Pass, Band Stop, FIR filters based on Magnitude response features including: pass band ripple, stop band ripple, transition width and bandwidth. Choose the proper window and filter order Understand equiripple FIR filter design. Implement FIR filter using the TMS320C6711 DSK B) Lab Report For lab report #4, in addition to: the traditional well formatted cover page, the signed pages of this lab, the conclusion, 1

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students are expected to: include a screen capture of waveforms insert their C/C++ source codes, The Design steps for the filters etc. C) FIR Filter Design Fig 1 represents the magnitude response of a digital ideal low pass filter with cut-off frequency of f 1 . 1 0.2 0.4 0.6 0.8 f 1 1 H(f) f Fig 1: Magnitude Response of an ideal Low Pass filter By using the Inverse Discrete Time Fourier Transform, we have: - = 1 1 2 ) ( ) ( df e f H n h fn j π - = 1 1 2 ) ( f f fn j df e n h π ) ( 2 1 ) ( 1 2 1 2 f j f j e e n j n h π π π - - = n n f n h π π ) 2 sin( ) ( 1 = Fig 2 shows the impulse response of the ideal response filter. 2
Fig 2: Impulse Response of the Ideal Low Pass filter The ideal low pass filter will be impossible to implement because: First, it is non causal. 0 for 0 ) ( < n n h Second, it has infinite number of elements. As a result, it can not be converted into a non recursive difference equation. To find a usable filter, the solution, therefore, is to truncate it from – N to + N and to right shift it to make the result causal as illustrated in Fig 3: 0 5 10 15 20 25 30 1 Fig 3: Truncated and shifted impulse response 3

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However, in that case, the magnitude response is no longer ideal. The elimination of terms has resulted into a degradation of the magnitude response. In general, it is no longer flat in the pass band, nor in the stop band. In addition, the width of the transition region is no longer zero. The general form of the magnitude response is shown in Fig 4. Fig 4: General form of the Magnitude Response of the Truncated Shifted Impulse Response. p δ is the maximum amplitude of the pass band ripple. s δ is the maximum amplitude of the stop band ripple. F p is the pass band edge frequency in Hz. F s is the stop band edge frequency in Hz. F s - F p gives the transition width. p δ , s δ , F p, F s, are called the features of the filter. Note that Fp does not correspond to the –3dB cut-off Frequency F 1 . 1.- Windowing Obviously, the higher N , the closer the magnitude response is to the ideal filter. In practice, we want to have the lowest possible value of N that satisfies a given set of features. The goal is to find a window w(n) , defined as: 0 ) ( n w for 2 1 - N n , 4
0 ) ( = n w for 2 1 - N n , such that ) ( ). ( ) ( 1 n h n w n h = satisfies the filter features for the minimum value of N .

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