QEDesign Capabilities: Infinite Impulse Response (IIR) Digital Filter Design

IIR digital filter design means that the sample output is a function of previous outputs as well as the current and previous input samples. The transfer function for such a filter has both poles and zeros. The poles must be within the unit circle in the Z-domain for a stable filter.

IIR filters can be designed in the analog domain (S plane) and then mapped to the digital domain (Z plane) or they can be designed directly in the Z plane.

	QEDesign will design lowpass, highpass, bandpass and bandstop IIR filters in the analog domain. Allpass IIR filters with arbitrary group delay are designed directly in the Z plane.
After choosing one of the IIR filter types, the user defines the filter specifications such as sampling frequency, pass and stop bands, and ripple.
	QEDesign then offers a selection of 5 types of prototype filters: Butterworth, Tschebyscheff, Inverse Tschebyscheff, Elliptic and Bessel, and suggests the filter order required to meet the filter specification. The user selects the prototype filter of choice (and the suggested filter order or a new value).
QEDesign then graphs magnitude, log magnitude, poles and zeros, impulse response, phase, group delay, and step response
	The transformation method into the digital domain is user selectable from bilinear transformation, impulse variant, or matched z-transform. Phase equalization is available or may be disabled.
Each of the design calculations requires large numbers of numerical calculations. In order to provide accurate coefficients for any filter order, QEDesign performs all design calculations in at least 64-bit floating point. Some very critical calculations in QEDesign 2000 for the Sun Workstations are performed in 128-bit precision. After calculating the coefficients with great accuracy, the coefficients must be quantized to a specific word length for implementation in a digital signal processor.
QEDesign provides complete quantization analysis. Quantizing the coefficients perturbs the location of the poles and zeros, so QEDesign shows the effects of this perturbation in the graphical displays of the filter characteristics. QEDesign also provides detailed analysis of the effects of finite arithmetic operations and can compute the output noise power, the least significant bit without error and the dynamic range of the filter.

Output reports show design details such as all transformations from normalized lowpass filter to desired filter coefficients.

QEDesign Capabilities: Finite Impulse Response (FIR) Digital Filter Design

Finite Impulse Response (FIR) Design means that the sample output is a function of the current and previous input samples only. Previous output samples do not in any way affect the current sample output. The transfer function for this type of filter consists of zeros only and as a result, FIR filters are always stable.

FIR filters are normally assumed to be linear phase i.e. the group delay is constant. This is true only if the filter coefficients have certain symmetries. QEDesign will create linear phase filters only, thus all FIR filters are either symmetric or antisymmetric about their center point.

There are several methods of designing FIR filters. QEDesign supports the most useful methods - window design and Parks-McClellan design.

Since all frequency functions are periodic on the unit circle of the z-domain, the magnitude and phase are periodic functions in the frequency domain. Thus it is possible to represent these functions as a Fourier series with the coefficients of the Fourier series representing the coefficients of the filter. To form a causal filter, the Fourier series is truncated and shifted.

The truncation of the Fourier series causes a phenomenon called the ``Gibbs effect''. This is a spike that occurs wherever there is a discontinuity in the desired magnitude of the filter. To counteract this, the filter coefficients are convolved in the frequency domain with the spectrum of a window function thus smoothing the edge transitions at any discontinuity. This convolution in the frequency domain is equivalent to multiplying the filter coefficients with the window coefficients giving the final filter coefficients.

QEDesign provides a large number of windows with both fixed and variable falloff to the first sidelobe in the magnitude response.

Parks-McClellan (Equiripple)

The Parks-McClellan design method uses an optimization algorithm called the Remez Exchange Algorithm. This type of design normally produces equiripple designs whereby the ripples in the passbands and stopbands are of equal height in any one band.

QEDesign has options for most filter types to alter this characteristic and allows rolloff values to be specified in 3dB increments. The optimization algorithm utilizes 64-bit precision arithmetic for all calculations. This is essential in the design of long filters.

Both types of FIR design (window functions and Parks-McClellan, with orders up to 8192) allow specification of either symmetric or antisymmetric filters. This, coupled with the option of specifying transition band functions, can lead to unique designs such as antisymmetric bandpass filter with root raised cosine transition functions.

	QEDesign allows for the design of the following FIR filter types: lowpass, highpass, bandpass, bandstop, differentiator, multiband, Hilbert transform, arbitrary magnitude, halfband, raised cosine, and root raised cosine.
QEDesign has the following FIR window functions available to the designer: rectangular, Hanning (Hann), Hamming, triangular, Blackman, exact Blackman, 3 term cosine, 3 term cosine with continuous 3rd derivative, minimum 3 term cosine, 4 term cosine, 4 term cosine with continuous 5th derivative, minimum 4 term cosine, good 4 term Blackman Harris, Harris flat top, Kaiser, Dolph-Tschebyscheff, Taylor, and Gaussian.
	FIR filter response is automatically graphed in the following plots: Magnitude Log Magnitude Impulse Response Step Response

Miscellaneous features available when designing FIR filters with QEDesign:

• Coefficient Quantization from 8 to 32 bits
• Reports show design details
• Filters can be designed for a nominal gain of 1 or maximum gain of 1
• Sin(x)/x Compensation
• Comb filter compensation
• Specification of Transition Regions on Selected Filter Types
• Choice of Symmetric/Antisymmetric FIR Filters

QEDesign Capabilities: System Analysis

The System Analysis section of QEDesign allows one to determine the characteristics (Magnitude, Phase, Group Delay, Impulse Response, Pole/Zero locations, and Step Response) of a given transfer function.
	Z-domain transfer function are inputted as a ratio of polynomials, zeros & poles, product of second order sections, sum of second order sections, symmetric FIR filter, or antisymmetric FIR filters.
S-domain transfer functions are specified in the as a ratio of polynomials, zeros and poles, or a product of second order sections.

QEDesign Capabilities: Graphical Design Capability

	A unique feature of QEDesign is the ability to graphically design a filter by adding, deleting or moving  poles and zeros on a plot. This design capability is required when filters that cannot be specified in a conventional manner. This feature also builds intuition on the result of placement of poles and zeros in the z domain.
QEDesign allows placement and movement of poles and zeros via mouse input, while simultaneous displaying of system responses. The software allows zoom-in/out capability for precise placement of poles/zeros and viewing responses in either rectangular or polar coordinates.

Document Index

QEDesign Capabilities: Code Generators

Momentum Data Systems offers a complete line of Code Generators to complement QEDesign's filter design capabilities. These code generators are designed to work seamlessly with QEDesign and provide the ability to produce assembly code quickly and easily.

The code generation module is accessible through a pull-down menu and reads coefficient files generated by QEDesign. It then creates highly optimized assembly language programs for both IIR and FIR filters.

General Features

• Modular programs for easy modification of input/output programs
• Complete programs including interrupt processing and handling of analog input/output

To view a list of available code generators click here