DSP for MATLAB and LabVIEW, Volume III: Digital Filter by Forester W. Isen
By Forester W. Isen
This publication is quantity III of the sequence DSP for MATLAB™ and LabVIEW™. quantity III covers electronic filter out layout, together with the explicit subject matters of FIR layout through windowed-ideal-lowpass clear out, FIR highpass, bandpass, and bandstop clear out layout from windowed-ideal lowpass filters, FIR layout utilizing the transition-band-optimized Frequency Sampling approach (implemented by way of Inverse-DFT or Cosine/Sine Summation Formulas), layout of equiripple FIRs of all usual varieties together with Hilbert Transformers and Differentiators through the Remez alternate set of rules, layout of Butterworth, Chebyshev (Types I and II), and Elliptic analog prototype lowpass filters, conversion of analog lowpass prototype filters to highpass, bandpass, and bandstop filters, and conversion of analog filters to electronic filters utilizing the Impulse Invariance and Bilinear remodel ideas. sure clear out topologies particular to FIRs also are mentioned, as are basic FIR forms, the brush and relocating common filters. the full sequence comprises 4 volumes that jointly disguise uncomplicated electronic sign processing in a pragmatic and obtainable demeanour, yet which still comprise all crucial starting place arithmetic. because the sequence identify implies, the scripts (of which there are greater than two hundred) defined within the textual content and provided in code shape (available through the web at www.morganclaypool.com/page/isen) will run on either MATLAB™ and LabVIEW™. desk of Contents: rules of FIR layout / FIR layout options / Classical IIR layout
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Extra info for DSP for MATLAB and LabVIEW, Volume III: Digital Filter Design
To compute S, which is the sum of x2 through x9 , add x9 to S, and subtract x1 . Once S is 22 CHAPTER 1. PRINCIPLES OF FIR DESIGN in hand, of course, S can be computed by adding x10 and subtracting x2 , and so forth. Phrased mathematically, this would be: S[n] = S[n − 1] + xn − xn−N This simple recursion formula can greatly reduce computational overhead when N gets to be very large. Since a Moving Average ﬁlter has an impulse response which consists of samples of a cosine of frequency zero, we would expect orthogonal behavior toward signals having an integral number of cycles in the length of the MA ﬁlter.
21: (a) Test signal, bipolar pulses in white noise (see text); (b) Test signal ﬁltered with a matched ﬁlter using the function conv; (c) Test signal ﬁltered with the matched ﬁlter using a recursive algorithm. 707j 5. 65j] as one of its zeros. Evaluate the magnitude and phase response of the resultant linear phase ﬁlter to verify its phase linearity. 6. (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.
Filter length is adjusted as necessary to achieve desired roll-off rate. Other ﬁlters such as highpass, bandpass, and notch can be generated starting with one or more lowpass ﬁlters. , frequencies deﬁned as 2π k/L with k = 0:1:L-1, for example) are speciﬁed, a linear phase factor is imparted, and the inverse DFT is computed to obtain the ﬁlter’s impulse response. 8. DESIGN METHODS 19 as the superposition of symmetrical cosines or sines, having frequencies conforming to one of two orthogonal systems.