Design multistage halfband IIR decimators.

Design classic IIR filters. The initial focus is on the situation for which the critical design parameter is the cutoff frequency at which the filter's power decays to half (-3 dB) the nominal passband value.

Use some of the key features of the generalized Remez FIR filter design function. This function provides all the functionality included in FIRPM plus many additional features showcased here.

Design peaking and notching filters. Filters that peak or notch at a certain frequency are useful to retain or eliminate a particular frequency component of a signal. The design parameters for the filter are the frequency at which the peak or notch is desired, and either the 3-dB bandwidth or the filter's Q-factor. Moreover, given these specifications, by increasing the filter order, it is possible to obtain designs that more closely approximate an ideal filter.

Design filters given customized magnitude and phase specifications. Custom magnitude and phase design specifications are used for the equalization of magnitude and phase distortions found in data transmission systems (channel equalization) or in oversampled ADC (compensation for non-ideal hardware characteristics for example). These techniques also allow for the design of filters that have smaller group delays than linear phase filters and less distortion than minimum-phase filters for a given order.

Design least Pth-norm FIR filters with the FIRLPNORM function. This function uses a least-Pth unconstrained optimization algorithm to design FIR filters with arbitrary magnitude response.

Design optimal IIR filters with arbitrary magnitude response using the least-Pth unconstrained optimization algorithm.

Design lowpass FIR Nyquist filters. It also compares these filters with raised cosine and square root raised cosine filters. These filters are widely used in pulse-shaping for digital transmission systems. They also find application in interpolation/decimation and filter banks.

Design filters for decimation and interpolation. Typically lowpass filters are used for decimation and for interpolation. When decimating, lowpass filters are used to reduce the bandwidth of a signal prior to reducing the sampling rate. This is done to minimize aliasing due to the reduction in the sampling rate. When interpolating, lowpass filters are used to remove spectral images from the low-rate signal. For general notes on lowpass filter design see the example on Designing Low Pass FIR Filters

Design arbitrary group delay filters using the fdesign.arbgrpdelay filter designer. This designer uses a least-Pth constrained optimization algorithm to design allpass IIR filters that meet a prescribed group delay.

Design digital fractional delay filters that are implemented using Farrow structures. Digital fractional delay (fracDelay) filters are useful tools to fine-tune the sampling instants of signals. They are, for example, typically found in the synchronization of digital modems where the delay parameter varies over time. This example illustrates the Farrow structure, a popular method for implementing time-varying FIR fracDelay filters.