QEDesign is an easy-to-use, multi-platform advanced digital filter design package. It is completely menu-driven and user intuitive, affording almost a non-existent start-up and learning curve. QEDesign performs complex mathematical computations for filter design, provides superior graphical displays, and generates comprehensive design reports.

Screen Shot from QED 1000 for Windows 95/NT

QEDesign Series features include:

• completely menu-driven system
• extensive error-checking
• extensive on-line help features
• use of 64-bit floating point for all calculations
• use of 128-bit floating point for critical design areas
• coefficient quantization variable from 8 to 32 bit
• coefficient scaling
• recycling of input for comparative analysis
• tiled and stacked graphic displays
• specification file for retention of previously designed filters
• transfer function analysis

Document Index

QEdesign Capabilities

• Infinite Impulse Response Digital Filter Design
• Finite Impulse Response Digital Filter Design
• System Analysis
• Graphical Design Capability
• Code Generators

Platform and Functionality Tables

• Supported Platforms
• Supported Filter Types
• Maximum Filter Order
• IIR Analog Prototypes
• Digital Transformation Methods
• IIR Realization Methods for bilinear and matched z-transform designs
• FIR Window Functions
• System Analysis
• Compensation Features
• Plot Options
• Miscellaneous

QEDesign Capabilities

• Infinite Impulse Response Digital Filter Design
• Finite Impulse Response Digital Filter Design
• System Analysis
• Graphical Design Capability
• Code Generators

Infinite Impulse Response Design

Infinite Impulse Response (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 provides five types of analog filter prototypes and three methods of transforming an S plane design to the digital domain. QEDesign also provides an allpass filter with arbitrary group delay capability. This filter is designed directly in the Z plane.

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.

• Lowpass, Highpass, Bandpass, Bandstop Filters, Arbitrary Group Delay
• Filter orders:
  • Lowpass 80
  • Highpass 80
  • Bandpass 160
  • Bandstop 160
  • Arbitrary Group Delay 160
• Analog Prototype Filters:
  • Butterworth
  • Tschebyscheff
  • Inverse Tschebyscheff
  • Elliptic
  • Bessel
• Digital Transformation methods:
  • Bilinear Transformation
  • Impulse Invariant
  • Matched Z-Transform
• Optional Phase Equalization
• Graphical Output includes:
  • Magnitude
  • Log Magnitude
  • Poles and Zeroes
  • Impulse Response
  • Phase
  • Group Delay
  • Step Response
• Quantization Features
  • Quantize Coefficients
    (8-32 bits)
  • Coefficient Scaling to prevent overflow
  • Computation of Dynamic Range
  • Computation of Least Significant Bit in Error
  • Output Noise Power Calculation
  • Analysis of Finite Arithmetical Operations
• Coefficients can be scaled for the following realizations:
  • Cascade Form 2 for fixed point implementation
  • Transpose of Cascade Form 2 for fixed point implementation
  • Parallel Form 1 for fixed point implementation
  • Cascade and parallel forms for floating point implementation
  • Direct form (ratio of polynomials)
• Reports show design details such as all transformations from normalized lowpass filter to desired filter coefficients

Finite Impulse Response 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) 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.

• Filter Types
  • Lowpass
  • Highpass
  • Bandpass
  • Bandstop
  • Differentiator
  • Multiband
  • Hilbert Transformer
  • Arbitrary Magnitude
  • Halfband
  • Raised Cosine
  • Root Raised Cosine Filters
• Filter Orders
  • Parks-McClellan 8192
  • Window Design 8192
• Available Window Functions:
  • 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
  • Gaussian
• Graphical output includes:
  • Magnitude
  • Log Magnitude
  • Impulse Response
  • Step Response
• Coefficient Quantization from 8-32 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

System Analysis

The System Analysis section of the system allows one to determine the characteristics (Magnitude, Phase, Group Delay, Impulse Response, Pole/Zero locations, and Step Response) of a given transfer function.

The transfer function can be input in the z-domain as:

• A ratio of polynomials
• Zeros & Poles
• Product of second order sections
• Sum of second order sections
• Symmetric FIR Filter
• Antisymmetric FIR Filter

A transfer function specified in the s-domain (i.e. Analog Transfer function) can be specified as:

• Ratio of Polynomials
• Zero and Poles
• Product of second order sections

Graphical Design

A unique feature is the graphical design via adding or deleting poles and zeros graphically and moving existing poles and zeros. This design capability is sometimes needed to design 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.

Placement of poles and zeros via mouse input, simultaneous display of system responses while moving poles or zeros.

Selection of either rectangular or polar coordinates and zoom-in/out capability for precise placement of poles/zeros.

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 provides 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

The following hardware platforms are currently supported:

• PC (Win95/NT)
• Engineering workstations (Xwindows/Motif)

Three QEDesign systems are available:

• QED - Lite:        a basic (student version) filter design system available for Windows95.
• QEDesign 1000: a more sophisticated system with extended features.
• QEDesign 2000: a premier filter design system for engineering workstations.

The following tables indicate specific functionality for each version of QEDesign:

• Supported Filter Types
• Maximum Filter Order
• IIR Analog Prototypes
• Digital Transformation Methods
• IIR Realization Methods for bilinear and matched z-transform designs
• FIR Window Functions
• System Analysis
• Compensation Features
• Plot Options
• Miscellaneous