DSP Application on One Dimension Signal

IEEE Paper Review: Implementation of a modem based on Quadrature Amplitude Modulation using TMS320C6201 DSP
Authors: N Dahnoun and D R Clewer
Publisher: IEEE
Published in: IEE Colloquium on DSP Chips in Real-Time Instrumentation and Display Systems
Location: Leicester, UK,
Date of Conference: 24 September 1997

Summary: 
Modems have traditionally been used to enable data communications via PSTN. This is severely band limited channel, requiring use of highly bandwidth efficient modulation schemes such as Quadrature Amplitude Modulation (QAM) combined with forward error correction and data compression in order to achieve bit rates up to 56 Kbps. The advances in DSP technology have recently enabled these bits rate to be achieved in commercial equipment at a reasonable cost. TMS320C6201 device boasts a maximum of 1600 MIPS at a clock speed of 200 MHz which is said to be more than a magnitude faster than any other fixed-point DSP. Cable modems allowing 36 Mbps transmission rates could be implemented using the same. Each module in transmitter as well as receiver was tested individually by writing a test program to read data in from a file, run the module and write the results on an output file. The data output were compared with expected output to judge failure and success of the DSP processor. To conclude, it was found that programming large functions in C on the DSP processor is both quick and easier than programming in assembler. 

Link: http://ieeexplore.ieee.org/document/659698/


Patent Review: Method for generating modern transmission signals with quadrature amplitude modulation.
Application Number: 06/136733 
Application Date: 04/27/1982 
Filling Date: 04/02/1980 
Inventors: Gockler, Heinz and Hofmeister, Hagen

Summary: 

The present invention relates to a method for generating modem transmission signals with quadrature amplitude modulation (QAM) in which scanned values of elementary bandpass signals are formed in digitally coded form, the elementary bandpass signals are weighted with coefficients depending on the information to be transmitted and the modem transmission signals are formed by superposition of the thus weighted elementary bandpass signals. It is therefore the object of the present invention to provide a method for generating modem transmission signals which operates with less calculating operations and thus enables the circuit to operate at a greater speed and with greater accuracy. The above object is accomplished according to one embodiment of the invention in that in a method for generating modem transmission signals with quadrature amplitude modulation (QAM). Another advantage of the invention is that in the case of m-ASK where m=2, 3, 4, . . .  the elementary bandpass signals are additionally weighted with factors corresponding to the amplitude stages characteristic for the information to be transmitted.

Link: http://www.freepatentsonline.com/4327439.html

 

Basic Operations on DSP Processor

The main aim of this experiment was to make us familiar with the DSP processors and to perform basic arithmetic and signal processing operations.
In this experiment basic convolution operation was performed on Texas Instruments C2000 TMS320F28335 DSP processor. The code was written on Code Composer studio which is used as a platform for implementing and debugging the codes. The advantage of using DSP processor is that, it is capable of handling large mathematical operations and also real time data can be processed with higher speed. For emulation XDS100v2 USB Emulator was selected. The output of the instructions was stored in the registers. In order to obtain the real time values of the register, the debugging functionality of the software was use.

Design of FIR filter using Frequency Sampling Method

Frequency sampling method is an alternative method to design FIR filter.

Frequency sampling method:
In this experiment various parameters such as passband attenuation, stop attenuation, passband frequency and stopband frequency and sampling frequency are passed as input. In this method the desired frequency response which is given as Hd(w) is sampled at w=2*pi*k/N where N is the length of the signal. The frequency sampled obtained are thus taken as DFT coefficients H[k].
FIR filter response is now obtained by taking Inverse Discrete Fourier Transform of H[k]. The results were verified by comparing the stopband and passband attenuation from the magnitude and phase spectrum which were plotted.

FIR filter Design using window Method

FIR filter Design using window Method

Depending upon the value of passband attenuation and stopband attenuation, appropriate window function was chosen from Hanning, Hamming, Blackman, Rectangular and Barlett.We have implemented the code in Scilab. In case of FIR filter the phase response of the filter varies linearly with the frequency thus the output of the filter is delayed version of the input by some constant and there is no distortion in the output. 

Design of Chebyshev Filter

Design of Chebyshev Filter.
The design procedure of chebyshev filter is very smiliar to that of Butterwoth Filter. In this experiment we implemented the Chebyshev Filter using BLT method. The parameters which were earlier used for design of butterworth filter are used for chebyshev filter. The magnitude response of chebyshev filter has ripple in passband depending upon the order of the filter and has monotonic response in stopband.

Design of Butterworth filter

Design of Butterworth Filter
This was the first experiment from which we started implementing the code in Scilab. Scilab is a software which is very similar to that of MATLAB. The biggest advantage of using Scilab software is that, it is an open source software. Initially we downloaded the Scilab software in all the PC's.
In this experiment various parameters such as passband attentuation, stopband attenuation, stopband frequency and passband frequency were passed as inputs and the code was implemented in such a way that it would calculate the order of the filter as well as the transfer function of the filter in Z domain. The steepness of the curve depends upon the order of the filter. Butterworth filter has monotonic passband as well as monotonic stopband.

Fast Fourier Transfrom

An algorithm for fast computation of DFT is FFT(Fast Fourier Transform).The FFT algorithm divides the N-point DFT input signal into 2 parts-even and odd signal

We performed 4-point and 8-point FFT. Then we verified the answer by performing Inverse FFT for both.

Later, number of calculations involved in FFT and DFT were compared and we found that very fewer calculations are required for FFT. Hence, FFT is used for parallel processing as it improves operational efficiency. 

  

Filtering of Data sequence

In order to reduce the delay and the data latency obtained during long data sequences overlap add and overlap save method is employed. These methods do not require the entire data to be present before carrying out the convolution. In case of overlap add method, the entire signal is divided into small length signals and the convolution of the signals are carried out with the response of the system. After carrying out the convolution the overlap portion is added to get the output. In case of overlap save method, the overlapped portion is saved to get the result. The result is same as that of time domain convolution. This methods are used to obtain the output of the system. 

Discrete Fourier Transform

DFT (Discrete Fourier Transform) is carried out to overcome the limitation of Fourier series as well as DTFT.
The programming language used in this experiment was C. For DFT(Discrete Fourier Transform) experiment we had considered 2 cases. The first case included calculations of 4 point DFT of given input signal. The second case had calculation of 8 point DFT of the same input signal x[n]. Magnitude spectrum was plotted for both the cases. The magnitude spectrum of 8 point signal has more resolution as compared to that of 4 point signal. We also performed the inverse Discrete Fourier transform of the same signal.

Linear and Circular Convolution and Correlation

The aim of this experiment was to study linear convolution, circular convolution and linear convolution using circular convolution and correlation of signals.
Convolution is an mathematical expression used to express the relation between input and output of a system.
Mathematically, Linear convolution is expressed as y[n]=x[n]*h[n]
Where x[n] is the input to the system and h[n] is the impulse response of the system.
Linear convolution is use to find the output of the system.
The length of the output signal obtained was the one less than the addition of the length of the 2 input signals. 
In case of Circular convolution the length of the output signal is chosen as maximum length of both the signals.
Circular convolution gives alliased output.
Correlation is use to find the degree of similarity of two signals.
Auto-correlation is an Even signal.