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Lesson_9 - EEL 3135 Signals and Systems Dr Fred J Taylor...

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EEL 3135: Signals and Systems Dr. Fred J. Taylor, Professor Lesson Title: FIR Filters Lesson Number: 09 (Section 5-1 and 5-2) Background: One of the fundamental tools that a contemporary engineer is to master is the filter. Filters are usually considered to be frequency selective devices. Linear filters have the ability of modify the amplitude and phase of a signal, but create no new frequencies. A non-linear filter can also generate new frequencies. Filters can also be classified by their technology in that there are continuous-time (analog) filters, discrete-time filters, and digital filters. Analog filters are fashioned using resistors, capacitors, inductors, and Op Amps. Discrete-time filters are more rare but do appear in the form of switched capacitor filters. Digital filters employ digital components. The study of digital filters is part of a branch of engineering called digital signal processing (DSP). DSP is a relatively young branch of engineering and, by its very definition, post-dates the introduction of digital technology. With the advent of the 1 st generation DSP microprocessors (DSP μ p) beginning in the late 1970's and early 1980’s, DSP began to replace traditional analog signal processing systems and subsystems. The popularity and importance of DSP has continued to grow ever since. DSP has, in fact, entered the laypersons vocabulary as evidence by the marketing vocabulary of personal electronic communication and entertainment systems. It is now considered to be a discipline unto itself replete with its own mathematics, analysis and synthesis methodology, and technology. Some of the core-competent DSP application areas include: General Purpose Graphics Filtering (Convolution) Rotation Detection (Correlation) Image transmission and compression Spectral analysis (Fourier transforms) Image recognition Adaptive filtering Image enhancement Instrumentation Control Waveform generation Servo control Transient analysis Disk control Steady-state analysis Printer control Biomedical instrumentation Engine control Information systems Guidance and navigation Speech processing Vibration (modal) control Audio processing Power system monitors Voice mail Robots Facsimile [FAX] Others Modems Radar and sonar Cellular telephones Radio and television Modulators, demodulators Music and speech synthesis Line equalizers Entertainment Data encryption Spread-spectrum Digital and LAN communications 1
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EEL 3135: Signals and Systems Dr. Fred J. Taylor, Professor In Chapter 5, finite impulse response (FIR) filters are considered. They are a class of digital filter that is based on feedforward information processing (only). Later feedback will be introduced and another class of filter, called infinite impulse response filter will result. In its most simplic form, a single-input single-output (SISO) filter is defined in terms of a mathematically mapping as shown in Figure 1. The general filter presented in Figure 1 represents any transformation of an input signal x[k] into an output signal y[k].
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