FilterDesign_note - EE338DiscretetimeSignalsandSystems

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1 EE 338 Discrete time Signals and Systems Part V: Digital Filters and Filter Design 1. Basics of digital filters a. Frequency response ܪሺ߱ሻ : a periodic function of ߱ with period . i. Low frequency: 0, േ2ߨ, േ4ߨ, ڮ , High frequency: േߨ, േ3ߨ, േ5ߨ, ڮ ii. Gain and attenuation: ܩܽ݅݊ ൌ 20 log ଵ଴ |ܪሺ߱ሻ|, Attenuation = Gain b. Ideal frequency selective filters i. Ideal low pass filter with cutoff frequency ߱ ܪ ூ௅௉ ሺ߱ሻൌ൜ 1 |߱|൑߱ ൑ |߱|൑ߨ ூ௅௉ ሺ݊ሻ ൌ ݏ݅݊ܿ ቀ ௡ఠ ቁൌ൝ ݊ൌ0 ୱ୧୬ ሺఠ ௡ሻ గ௡ ്݊0 Low pass: pass the low freq. comp. ( ൑߱ ) and reject the high freq. comp. ( ൒߱ ) Ideal: constant magnitudes in the pass and the stop bands, and sharp transitions between the pass and the stop bands. ܪ ூ௅௉ ሺ߱ሻ is a real and symmetric function of ߱ (a zero phase filter), ݄ ூ௅௉ ሺ݊ሻ is also real and symmetric. Æ ݄ ூ௅௉ ሺെ݊ሻൌ݄ ூ௅௉ ሺ݊ሻ is non causal and is an IIR filter ii. Ideal high pass filter with cutoff frequency
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FilterDesign_note - EE338DiscretetimeSignalsandSystems

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