This book is a gentle introduction to digital filters, including mathematical theory, illustrative examples, some audio applications, and useful software starting points. The theory treatment begins at the high-school level, and covers fundamental concepts in linear systems theory and digital filter analysis. Read Free Introduction To Digital Signal Processing And Filter Design 7 Digital Filter Realizations 265 7.1 Direct Form, 265 7.2 Canonical Form, 271 7.3 Cascade Form, 277 7.4 Cascade to Canonical, 284 7.5 Hardware Realizations and Circular Buffers, 293 7.6 Quantization Effects in Digital Filters, 305 7.7 Problems,Home > Engineering » Electrical Engineering » Signal ProcessingDesign of All-pass Digital Filters An all-pass lter is an IIR lter with a constant magnitude function for all digital frequency values. For a transfer function H(z) to represent an all-pass lter is that for every pole pk rkej, there is a corresponding zero zk 1 rk ej. TheSignal filtering: Why and how Prevent over-filtering by simultaneously optimizing loop tuning and filter parameters.Digital Filter Algorithms The digital filter equations are based on the following basic transfer function shown in the z domain: Y(z) H(z)X(z), where Y(z) is the filter output, X(z) is the filter input, and H(z) is the transfer function of the filter. H(z) can be expanded A digital filter can be pictured as a “black box” that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds.Therefore, the term “finite impulse response” is nearly synonymous with “no feedback”.However, if feedback is employed yet the impulse response is finite, the filter still is a FIR. A lack of feedback guarantees that the impulse response will be finite. 1.3 Why is the impulse response “finite?”In the common case, the impulse response is finite because there is no feedback in the FIR. 1.2 What does “FIR” mean?“FIR” means “Finite Impulse Response.” If you put in an impulse, that is, a single “1” sample followed by many “0” samples, zeroes will come out after the “1” sample has made its way through the delay line of the filter. FIR filters are one of two primary types of digital filters used in Digital Signal Processing (DSP) applications, the other type being IIR.
Digital Filter Software Starting Points1.6 How do FIR filters compare to IIR filters?Each has advantages and disadvantages. (See dspGuru’s IIR FAQ.) IIR filters use feedback, so when you input an impulse the output theoretically rings indefinitely. (The difference is whether you talk about an F-I-R filter or a FIR filter.) 1.5 What is the alternative to FIR filters?DSP filters can also be “Infinite Impulse Response” (IIR). 1.4 How do I pronounce “FIR?”Some people say the letters F-I-R other people pronounce as if it were a type of tree. This filter has a finite impulse response even though it uses feedback: after N samples of an impulse, the output will always be zero. Windows erase disk programOn most DSP microprocessors, the FIR calculation can be done by looping a single instruction. They are simple to implement. Put simply, linear-phase filters delay the input signal but don’t distort its phase. They can easily be designed to be “linear phase” (and usually are). 1.6.1 What are the advantages of FIR Filters (compared to IIR filters)?Compared to IIR filters, FIR filters offer the following advantages: ![]() (The overall gain of the FIR filter can be adjusted at its output, if desired.) This is an important consideration when using fixed-point DSPs, because it makes the implementation much simpler.1.6.2 What are the disadvantages of FIR Filters (compared to IIR filters)?Compared to IIR filters, FIR filters sometimes have the disadvantage that they require more memory and/or calculation to achieve a given filter response characteristic. Unlike IIR filters, it is always possible to implement a FIR filter using coefficients with magnitude of less than 1.0. They can be implemented using fractional arithmetic. The use of finite-precision arithmetic in IIR filters can cause significant problems due to the use of feedback, but FIR filters without feedback can usually be implemented using fewer bits, and the designer has fewer practical problems to solve related to non-ideal arithmetic. In practice, all DSP filters must be implemented using finite-precision arithmetic, that is, a limited number of bits. The number of FIR taps, (often designated as “N”) is an indication of 1) the amount of memory required to implement the filter, 2) the number of calculations required, and 3) the amount of “filtering” the filter can do in effect, more taps means more stopband attenuation, less ripple, narrower filters, etc. Tap – A FIR “tap” is simply a coefficient/delay pair. (If you put an “impulse” into a FIR filter which consists of a “1” sample followed by many “0” samples, the output of the filter will be the set of coefficients, as the 1 sample moves past each coefficient in turn to form the output.) Impulse Response – The “impulse response” of a FIR filter is actually just the set of FIR coefficients. 1.7 What terms are used in describing FIR filters? Delay Line – The set of memory elements that implement the “Z^-1” delay elements of the FIR calculation. (A “small” transition band results in a “sharp” filter.) The narrower the transition band, the more taps are required to implement the filter. Transition Band – The band of frequencies between passband and stopband edges. Most DSP microprocessors implement the MAC operation in a single instruction cycle. FIRs usually require one MAC per tap. When a new sample is added to the buffer, it automatically replaces the oldest one. Circular buffers are often provided by DSP microprocessors to implement the “movement” of the samples through the FIR delay-line without having to literally move the data in memory.
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