## What is Remez exchange algorithm?

The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the best in the uniform norm L∞ sense.

## What are the methods of filter design?

Advanced Filter Design Methods

Design Method | Function |
---|---|

Allpass filter (given group delay) | iirgrpdelay (DSP System Toolbox) |

Least P-norm optimal IIR | iirlpnorm (DSP System Toolbox) |

Constrained least P-norm IIR | iirlpnormc (DSP System Toolbox) |

Second-order IIR notch | iirnotch (DSP System Toolbox) |

**What is meant by optimum Equiripple design criterion?**

It is viewed as an optimum design criterion in the sense that the weighted approximation error between the desired frequency response and the actual frequency response is spread evenly across the passband and evenly across the stopband of the filter minimizing the maximum error.

**What is Chebyshev approximation?**

Chebyshev approximation is a part of approximation theory, which is a field of mathematics about approximating functions with simpler functions. This is done because it can make calculations easier. Most of the time, the approximation is done using polynomials.

### What is minimax polynomial?

The approximating polynomial which has the smallest maximum deviation from the true function. It is closely approximated by the Chebyshev polynomials of the first kind.

### What is filter design in DSP?

The design of a digital filter involves five steps: Specification: The characteristics of the filter often have to be specified in the frequency domain. For example, for frequency selective filters (lowpass, highpass, bandpass, etc.) the specification usually involves tolerance limits as shown above.

**What is Gibbs phenomenon in FIR filter?**

Truncating the impulse response introduces undesirable ripples and overshoots in the frequency response. This effect is known as the Gibb’s phenomenon. The Gibbs phenomenon effect manifests itself as a fixed percentage overshoot and ripple before and after an approximated discontinuity in the frequency response.

**Which filter is always stable?**

a) FIR Filter is always stable.

#### What are Chebyshev filters used for?

Chebyshev filters are used to separate one band of frequencies from another. Although they cannot match the performance of the windowed-sinc filter, they are more than adequate for many applications.

#### What is Chebyshev’s theorem and how is it used?

Chebyshev’s theorem is used to find the proportion of observations you would expect to find within a certain number of standard deviations from the mean. Chebyshev’s Interval refers to the intervals you want to find when using the theorem.

**What is Minimax search procedure in artificial intelligence?**

Mini-max algorithm is a recursive or backtracking algorithm which is used in decision-making and game theory. It provides an optimal move for the player assuming that opponent is also playing optimally. Mini-Max algorithm uses recursion to search through the game-tree.

**What is the Remez exchange FIR filter design method?**

The Remez Exchange FIR filter design method (also called the Parks-McClellan, or Optimal method) is a popular technique used to design high-performance FIR filters. [] To use this design method, we have to visualize a desired frequency response Hd (m) like that shown in Figure 5-30. [] Remez is pronounced re-‘m.

## What is Remez algorithm?

Remez algorithm is one of the Optimal filter design techniques that are used to design best filter for a given length of FIR filter using Equiripple design which is highly advantageous due to its response is near to the ideal frequency response with low order when compared to the window technique.

## What is the passband ripple value of the Remez design method?

(Some of the early journal papers describing the Remez design method used the equally valid expression –20 · log10 (dp) to define the passband ripple in decibels. However, Eq. (5-22) is the most common form used today.)

**How to design the ideal frequency response of a filter?**

The window method is used for designing ideal frequency response of desired filter is equal to 1 for the pass band and 0 for stop band and the filter impulse response is obtained by taking the Discrete Fourier Transform (DFT) of the ideal frequency response.