Digital Filter Design and Algorithm Implementation with Embedded Signal Processors

Electronic systems deal with signals that have a frequency spectrum with a wide range of frequency components. These frequency components require filter functions that may include isolation, rejection or attenuation depending on system implementation. Digital filters are systems that modify certain frequencies relative to others either by a digital computational process or by implementation of an algorithm. A band-limited signal which is continuos-time is sampled at the Nyquist rate and converted to discrete-time by a digital filter. This paper deals with the design of digital filters which include specification, approximation and realization of the desired properties of a causal discrete time system using a new generation of Intel 80C196 embedded controllers with digital signal processing capabilities. The 80C196, in addition to its register to register architecture, has a hardware based accumulator and multiply accumulate instructions suitable for signal processing. Key features of the instruction set to perform signal processing functions are described. Fast I/O operations and software implementation of digital filters in hard disk drive servo operations, optimized for performance and memory are discussed, along with a high level overview of both the architecture and software are discussed. Signal Processing with Filters Signals that have a frequency spectrum with a wide range of frequency components are transformed and manipulated with the input/output signal information during signal processing. Discrete time signal processing converts a continuos time signal into a sequence of samples which is a discrete time signal. Discrete time signals or digital signals appear mathematically as a sequence of numbers. Digital filters involve processing continuos time signals using discrete time signal processing. Digital signals have an independent variable with discrete values for both time and amplitude. Filtering consists of the modification of an input signal to a desired output signal. Digital filters, unlike analog filters, can be implemented by an algorithm. A continuos time input signal which is sampled appears as a sequence of numbers and is transformed to an output signal which is a digital signal. This digital signal can be transformed back to a continuos time signal after the signal processing is completed. Filters in general are used in a variety of applications in the form of low pass filters passing the lower frequency components, high pass filters passing the high frequency components and band pass filters that pass a certain range of frequencies while attenuating other frequencies of signals that are continuos in time and are band limited. Digital filters eliminate variations normally present in the case of analog filters due to analog components. The variations may be in the form of noise and voltage variations affecting the phase and magnitude response of the filter being implemented. Presently, fast fixed point and floating point operations which are normally used to implement discrete time signal processing are available on silicon. The digital filter implemented on a single integrated circuit is an easy to use programmable microprocessor such as an 80C196NU, that follows the specified magnitude and phase response of the filter in design, accurately and consistently. Signal processing that require transformation of signals and are impossible to implement using analog components are realized in the form of digital filters on silicon. The design of digital filters described here will be in the form of causal, time-invariant, linear systems. A system in which there is no output before the input is applied is stated to be a causal system. When an input h(t) in the form of an impulse response is applied to a system h(t) = 0 for all t < 0 In a time-invariant system there will be a shift in the output sequence of numbers for a delay applied in the input sequence. For example, a system with input x(t) and output y(t), for a delay ‘n’ applied to the input x(t-α) the output will be y(t-α) where α is the time shift.