Science universe: Physics articles

Analog Filters Here, we summarize three basic types of analog low-pass filters that can be used as prototype for designing IIR filters. For each type, we give the transfer function, its magnitude response, and the order N needed to satisfy the (analog) specification. We use H a ( s ) to denote the transfer function of an analog filter, where s is the complex variable in the Laplace transform. Each of these filters have all its poles on the left- half s plane, so that it is stable. We use the variable λ to represent the analog frequency in radians/second. The frequency response H a ( λ ) is the transfer function evaluated at s = j λ . The analog low-pass filter specification, as shown in Fig. 12.12 , is given by where λ p and λ s are the pass-band edge and stop-band edge, respectively. Butterworth Filters The transfer function of an N th-order Butterworth filter is given by order required to satisfy Eq. (12.8) is Inverse Chebyshev Filters (Type II Chebyshev Filters...

Introduction Digital filtering is concerned with the manipulation of discrete data sequences to remove noise, extract information, change the sample rate, and perform other functions. Although an infinite number of numerical manipulations can be applied to discrete data (e.g., finding the mean value, forming a histogram), the objective of digital filtering is to form a discrete output sequence y ( n ) from a discrete input sequence x ( n ). In some manner or another, each output sample is computed from the input sequence—not just from any one sample, but from many, in fact, possibly from all of the input samples. Those filters that compute their output from the present input and a finite number of past inputs are termed finit e impulse response (FIR), whereas those that use all past inputs are infinite impulse response (IIR). This chapter will consider the design and realization of both FIR and IIR digital filters and will examine the effect of finite wordlength arithmetic on impleme...