Both the lowpass to bandpass transformations and lowpass to bandstop

Both the lowpass to bandpass transformations and

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Both the lowpass to bandpass transformations and lowpass to bandstop transformations preserve arithmetic symmetry about the center frequency F 0 . If the band edges are [ F 1 , F 2 , F 3 , F 4 ] in increasing order, arithmetic symmetry means that and implies equal transition widths. If the transition widths are not equal, a band edge must be relocated to make both transition widths equal to the smaller width, 0 3 2 2 1 2 F F F F F
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77 All right reserved. Copyright © 2013. Sharifah Saon
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78 All right reserved. Copyright © 2013. Sharifah Saon Summary Impulse response of windowed filters
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79 All right reserved. Copyright © 2013. Sharifah Saon Recipe for window-based FIR filter design Normalize the analog design frequencies by the sampling frequency S . Obtain the band edges F p and F s of the lowpass prototype. Choose the lowpass prototype cutoff frequency as F C = 0.5( F p + F s ). Choose a window from Table in page 58 that satisfies A WS A s and A WP A s . Compute the window length N from F T = F s - F p = F WS C / N (with C as in Table at page 58). Compute the prototype impulse response, , Window h [ n ] and apply spectral transformations (if needed) to convert to required filter type. c c N nF c F n h 2 sin 2 1 5 . 0 N n
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80 All right reserved. Copyright © 2013. Sharifah Saon Example 6.9 ( FIR filter design by using windows ) a) Design FIR filter for each of the block filter ; with N = 5 and S = 10kHz. Filter 1: f p = 2kHz, f s = 1kHz, and Filter 2: f p = 1kHz, f s = 2kHz, with cosine window Filter 3: f s1 = 1kHz, f s2 = 6kHz, f p1 = 2kHz and f p2 = 4kHz, with Bartlett window b) Calculate the h [ n ] of this filter system. Filter 1 Filter 2 Filter 3 + - h [ n ]
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81 All right reserved. Copyright © 2013. Sharifah Saon Comparison between FIR and IIR filters
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Filter Specifications
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Filter Specifications Stopband Passband Transition band Brick wall Passband ripple Stopband ripple 0 Analog Relative Absolute Specifications dB 0 Passband edge Stopband edge Cutoff-frequency
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Filter Specifications Relative Specifications
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Analog Filter Specifications
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87 All right reserved. Copyright © 2013. Sharifah Saon An IIR digital low-pass filter is required to meet the following specifications: Passband ripple: ≤ 0.5 dB Passband edge: 1.2 kHz Stopband attenuation: ≥ 40 dB Stopband edge: 2.0 kHz Sample rate: 8.0 kHz Estimate the required filter order for a digital Butterwoth filter a digital Chebysev filter a digital elliptic filter
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88 All right reserved. Copyright © 2013. Sharifah Saon
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