ISBN-10: 1558608702

ISBN-13: 9781558608702

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**Sample text**

A) Design a comb ﬁlter having impulse response = [1,zeros(1, N),1] that is to give the maximum attenuation possible to a 60 Hz cosine wave sampled at 44,100 Hz. Determine N, then plot the log-magnitude spectrum of the signal after being ﬁltered by your comb ﬁlter. Repeat the ﬁltering 34 CHAPTER 1. PRINCIPLES OF FIR DESIGN and log-magnitude plot using values of N from three less to three more than the value you computed to verify that your value of N gives the best attenuation. (b) Repeat part (a), this time using as the signal to be attenuated the following: y = cos(120π t) + cos(360π t) + cos(600π t) where t = [0:1/(44,099):1].

The following m-code generates such an impulse response; change wc to control cutoff frequency and L to control impulse response length. Note that a true ideal lowpass ﬁlter impulse response is a continuous function of inﬁnite duration from t = -∞ to +∞; in this example, we are computing a ﬁnite number of samples of such a function. For the purposes of bandlimited discrete processing and digital ﬁltering, of course, this is acceptable. 2) where the window length is L, M = (L − 1)/2, 0 ≤ n ≤ L − 1, and WL [n] is generally a function FE [n] having even symmetry about M deﬁned as WL [n] = FE [n] n = 0:1:L − 1 0 otherwise The right side of Eq.

4 CASCADED LINEAR PHASE FORM Another possibility for a linear phase FIR is to form a cascade of linear phase, real coefﬁcient sections. A typical section would be fourth order, based around a linear phase quad of zeros, although for certain ﬁlters, some zeros might come in complex conjugate pairs lying on the unit circle, which would yield second-order real coefﬁcient sections. 0) as well as pairs of reciprocal-magnitude real zeros. 5 FREQUENCY SAMPLING Recall the formula for reconstructing the z-transform of a sequence x[n] of length N from N samples of the z-transform X[k] located at frequencies 2π k/N where k = 0:1:N − 1.

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