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 2048
- Window Design 2048
- 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
適用於
- PC (Win95/NT)
- Engineering workstations (Xwindows/Motif)
產品動態操作說明
按這裡 |
