Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
1998-12-31
2001-06-05
Mai, Tan V. (Department: 2121)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
C708S300000
Reexamination Certificate
active
06243729
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a system and method for increasing the operating speed of a finite-impulse-response (FIR) filter by taking full advantage of the Radix-N numbering system as implemented in a modified architecture, where N>4. The modified architecture relates particularly to applications having unequalized input data of an n-bit binary format, where n is >2.
BACKGROUND
A FIR filter may be included in the general class of devices referred to as digital signal processors (DSP). This does not mean that the FIR can operate only on digital signals, however. A “digital signal” is a signal that conveys a discrete number of values. Contrast the “analog signal,” i.e., a signal that conveys an infinite number of values. A signal having a digital form may be generated from an analog signal through sampling and quantizing the analog signal. Sampling an analog signal refers to “chopping” the signal into discrete time periods and capturing an amplitude value from the signal in selected ones of those periods. The captured value becomes the value of the digital signal during that sample period. Such a captured value is typically referred to as a sample. Quantizing refers to approximating a sample with a value that may be represented on a like digital signal. For example, a sample may lie between two values characterized upon the digital signal. The value nearest (in absolute value) to the sample may be used to represent the sample. Alternatively, the sample may be represented by the lower of the two values between which the sample lies. After quantization, a sample from an analog signal may be conveyed as a digital signal. This is the resultant signal upon which the FIR filter may operate.
Generally speaking, a DSP transforms an input digital signal to an output digital signal. For the FIR filter, the transformation involves filtering out undesired portions of the received digital signal. An original analog signal may be represented as a sum of a plurality of sinusoidal signals. Each sinusoidal signal oscillates at a particular and unique frequency. Filtering is used to remove certain frequencies from an input signal while leaving other frequencies intact.
A FIR filter is a device in which an input sample produces a finite number of output samples. After the finite number of samples expires, the FIR filter output is no longer affected by that particular input sample. Transversal filters, of which FIR filters may be a class, are filters in which a certain number of past samples are used along with the current sample to create each output sample.
FIR filters typically employ an instruction set and hardware design for programming of desired signal filtering. A program is a list of instructions which, when executed, performs a particular operation (i. e., a signal transformation). Programs executing on FIR filters often do so in “real-time”. Real-time programs are programs that must execute within a certain time interval. Regardless of whether a program executes in a large period of time or a small period of time, the result of executing the program is the same. However, if real-time programs attempt to execute in an amount of time longer than the required time interval, then they no longer will compute the same result. Programs executing on a FIR filter are real-time programs in that the instructions are manipulating a sample of a digital signal during the interval preceding the receipt of the next sample. If the program cannot complete manipulating a sample before the next sample is provided, then the program will eventually begin to “lose” samples. A lost sample does not get processed, and therefore the output signal of the FIR filter no longer contains all of the information from the input signal provided to the FIR filter.
A FIR filter may be programmed to modify signals. The number of instructions required to do this is relatively fixed. A FIR filter must be capable of executing this relatively fixed number of instructions on any given sample before the next sample of the series is provided.
Besides considering a FIR filter's throughput, all design parameters are associated with a cost. One important cost factor is the silicon area needed to manufacture the FIR filter. Those which are manufactured on a relatively small silicon die are typically less expensive than those requiring a large silicon die. Therefore, an easily manufacturable, low cost FIR filter is desirable.
FIR filters often include memory devices, such as registers, ROM or RAM, to store instructions and samples. It is typical that more transistors are used to form the memory devices than those used to form other FIR filter circuitry. Sometimes the memory-to-other transistor ratio can exceed 2:1. Therefore, it is also important to minimize the size of the included memory devices. However, the size and location of the memory device directly affects throughput. Memory devices configured on the same silicon substrate as the FIR filter may be accessed significantly faster than memories configured on separate substrates. Therefore, large memory devices configured on the same silicon substrate as the FIR filter are desired.
Die area may be maintained while increasing the effective size of the instruction memory by decreasing the size of individual instructions. One method of decreasing the size of an instruction is to encode the information in as few bits as possible. Unfortunately, these instructions require complicated decoding circuitry to determine which of the instructions is currently being executed. Such decoding circuitry also may require a large silicon area or a large amount of time to execute, or both. A cost-effective, high performance instruction set solution is therefore needed to enhance existing FIR filters.
Some features of FIR filters that are important to the design engineer include phase characteristics, stability (although FIR filters are inherently stable), and coefficient quantization effects. To be addressed by the designer are concerns dealing with finite word length and filter performance. When compared with other filter options such as infinite impulse response (IIR) filters, only FIR filters have the capability of providing a linear phase response and are inherently stable, i.e., the output of a FIR filter is a weighted finite sum of previous inputs. Additionally, the FIR filter uses a much lower order than a generic Nyquist filter to implement the required shape factor. This carries a penalty of non-zero inter-symbol interference (ISI), however.
Coefficient quantization error occurs as a result of the need to approximate the ideal coefficient for the “finite precision” processors used in real systems. The net result due to approximated coefficients is a deviation from ideal in the frequency response.
Quantization error sources due to finite word length include:
a) input/output (I/O) quantization,
b) filter coefficient quantization,
c) uncorrelated roundoff (truncation) noise,
d) correlated roundoff (truncation) noise, and
e) dynamic range constraints.
Input noise associated with the analog-to-digital (A/D) conversion of continuous time input signals to discrete digital form and output noise associated with digital-to-analog conversion are inevitable in digital filters. Propagation of this noise is not inevitable, however.
Uncorrelated roundoff errors most often occur as a result of multiplication errors. For example, in attempting to maintain accuracy for signals that are multiplied, only a finite length can be stored and the remainder is truncated, resulting in “multiplication” noise being propagated. Obviously, any method that minimizes the number of multiplication steps will also reduce noise and increase inherent accuracy.
Correlated roundoff noise occurs when the products formed within a digital filter are truncated. These include the class of “overflow oscillations”. Overflows are caused by additions resulting in large amplitude oscillations. Correlated roundoff also causes “limit-cycle effect” or small-amplitude oscillations. For systems with adequa
Brady III Wade James
Mai Tan V.
Swayze, Jr. W. Daniel
Telecky , Jr. Frederick J.
Texas Instruments Incorporated
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