数字信号处理第4章(南理工).pptVIP

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2018-05-14 发布于四川
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数字信号处理第4章(南理工).ppt

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DSP group chap4-ed1 DSP group Chap-3 4.1 Introduction Frequency translation Frequency translation: Any of the replicas in the lower frequency bands can be retained by passing gp(t) through bandpass filters with passbands: ---providing a translation of the original bandpass signal to lower frequency ranges. 4.4 Analog Lowpass Filter Design Filter Specification : Passband: Stopband: Passband edge frequency: ?p ; Stopband edge frequency: ?s . Frequency-Domain Characterization of the LTI DT System Peak passband ripple: ?p = ?20log10(1 ? ?p ) dB (4.35) Minimum stopband attentuation: ?s = ?20log10(?s) dB (4.36) Ripples are usually specified in dB as: Peak ripple value in the passband: ?p ; Peak ripple value in the stopband : ?s . Normalized specifications for analog lowpass filter The maximum value of the magnitude in the passband is assumed to be unity(1); Passband ripple: The maximum value of the magnitude in the passband Maximum stopband ripple: Two additional parameters Transition ratio/selectivity parameter: k 1 for lowpass filter Discrimination parameter: usually, Butterworth Approximation N-th order butterworth filter: also called a maximally flat magnitude filter Gain in dB: At dc, i.e., ? =0: At ? = ?c : ?c ---- 3dB cutoff frequency. Typical magnitude response with ?c =1 Two parameters: the 3-dB cutoff frequency ?c and the order N completely characterize a Butterworth filter. ?c and N are determined from : ?p, , ?s, 1/A. Obtain ?c and N Solve the equations of (4.40) Transfer function of Butterworth lowpass filter where The denominator DN(s) is known as the Butterworth polynomial of order N. Example analog lowpass Butterworth Filter Example 4.8 Determine the lowest order of a transfer function Ha(s) having a maximally flat characteristic with a 1-dB cutoff frequency at 1kHz a