Digital Signal Processing Reference
In-Depth Information
• Chapter 4 introduces correlation and the correlation sequence, orthogonality of sinusoids and
complex exponentials, sequence decomposition and reconstruction using correlation (i.e., the real
DFT), correlation via convolution, matched filtering, simple FIR filters, and the basic IIR using a
single pole or complex conjugate pole pairs.
1.5
CONTENTS OF VOLUME II IN THE SERIES
The second topic in the series covers standard digital frequency transforms and closely related topics.
• Chapter 1 begins with a short overview of the Fourier and Laplace families of transforms, calling
attention to the uses of each and the differences among them. The remainder of the chapter is
devoted to the Discrete Time Fourier Transform (DTFT), its properties, and its use in evaluation
of the frequency response of an LTI system.
• Chapter 2 introduces the
z
-transform, its properties, the inverse
z
-transform, transfer function
and various filter topologies (Direct, Cascade, Parallel, and Lattice Forms), and evaluation of the
frequency response of an LTI system using the
z
-transform.
• Chapter 3 covers the Discrete Fourier Transform (DFT), including the forward and reverse trans-
forms, properties, the Fast Fourier Transform (FFT), the Goertzel Algorithm, periodic, cyclic, and
linear convolution via the DFT, and DFT leakage. Computation of the IDFT (inverse DFT) via
DFT, computation of the DFT via matrix, and computation of the DTFT via the DFT, are also
discussed.
1.6
CONTENTS OF VOLUME III IN THE SERIES
The third topic in the series is devoted to digital filter design.
• Chapter 1 gives an overview of FIR filtering principles in general, and linear phase filter charac-
teristics in particular, and an overview of FIR design techniques.
• Chapter 2 covers FIR design via windowed ideal lowpass filter, frequency sampling with optimized
transition coefficients (as implemented by inverse DFT as well as cosine/sine summation formulas),
and equiripple design. Designs are performed for lowpass, highpass, bandpass, and bandstop filters,
as well as Hilbert transformers and differentiators.
• Chapter 3 is devoted to classical IIR design, including design of digital IIR filters starting from
analog prototype lowpass filters of the Butterworth, Chebyshev (I and II), and Elliptic types,
transformations from lowpass to other passband types in the analog domain, and analog-to-digital
filter transformation. The chapter concludes with a discussion of various filter design functions
provided by MATLAB and LabVIEW.
