DSP Apllication on One Dimensional Signal

IEEE Paper Review: Design of AM Modulation Signal Generator based on Matlab/DSP builder.               
Authors: Junshan Gao, Nan Liu, Xinghu Xu  
Publisher :- IEEE  
Published in: 2010 2nd International Conference on Industrial & information Systems

Summary - Design of traditional AM Modulator requires high hardware theoretical knowledge. Further to vary modulation index or modulating signal frequency, entire designed hardware is to be modified;there by increasing system cycle development & reducing usability of existing system. An alternative to this is Direct Digital Synthesis(DDS) is an all digital frequency synthesis technology.

DDS is a total digital frequency synthesizer,including phase accumulator,wave memorizer, conversion of D/A and LPF.

AM Modulation Signal Generator was first established using Matlab/Dsp builder. It was the simulated to check whether desired operation was achieved. It can then be converted to realize VHDL document for system level realization using RTL level code.

 

Paper - > http://ieeexplore.ieee.org.sci-hub.cc/document/5565794/?reload=true

Patent Review : Amplitude & Phase Modulator

Application No - PCT/US2001/043502

Patent No - WIPO Patent Application WO/2002/049300

Date of Patent - 06/20/2002

Inventors - Pehlke, David R., Hadjichristos, Aristotle, Camp Jr., William O

Summary - 

However, To ensure reliable wireless communication between hand held devices, Mobile terminals usually have significant constraints on overall operating power. 
An RF power amplifier circuit comprising of -  a power amplifier biased for saturated mode operation and operative to generate an RF output signal by amplifying a constant envelope RF input signal ; a modulator comprising a resistive load(voltage controlled resistor - Field Effect Transistor) for coupling an operating voltage input of power amplifier to a supply voltage.
An RF signal that includes frequency or phase information in addition to amplitude information may be separated into first and second signal components. The first signal is at the desired transmit frequency and has a constant amplitude envelope, but includes the phase or frequency modulation information of the original RF signal to be amplified.
The second signal is an amplitude modulation (AM) signal and represents the AM information in the original RF signal to be amplified.
 A balanced power amplifier circuit (2 - stage) is then required to combine 2 signals to recover original modulating signal.

Patent - > http://www.freepatentsonline.com/WO2002049300A2.pdf

Expt - 9 Basic Operations on DSP Processor

In this Lab session basic operation like convolution was performed on TI's C2000 DSP(Digital Signal Processor) TMS320F28335. The code was written on Code Composer Studio 3 in C language.Values of registers were noted down before and after each execution. The output of these instructions is seen using the JTAG debugger.For emulation XDS100v2 USB Emulator was selected.

These operations are similar to the ones in a regular processor but the DSP's hardware allows faster and more efficient execution of these instruction with the help of Multiply & Accumulate Unit (MLA).

Thus they are used mainly for signal processing applications where high speed computation is of prime importance.

Expt - 8 Digital FIR Filter Design using Frequency Sampling

It as an alternative method for implementation of FIR Filter Design.

The desired frequency response Hd(w) is sampled at discrete values of frequency to obtain H(k). A factor of 2*pi has to be added every time a sign change occurs in the magnitude of H(k). 

The final output sequence is obtained by Inverse Discrete Fourier Transform (IDFT).

Hd(w)----------------H(k)------------------h(n).

         
       (By sampling)           (By IDFT)

        

The frequency sampling realization of filter is computationally more efficient mainly because the sample values are symmetric about k = N/2.

Expt - 7 Digital FIR filter design using windowing method

The aim of the experiment was to design a Digital Filter using windowing method. Code was developed in Scilab, which asked user to enter Ap, As,wp & ws.  Depending upon the value of As, windowing function among Rectangular, Bartlet, Hamming, Hanning & Blackman was selected & order of the filter was computed using Transition width of windowing function.

Thus, Phase response varies linearly with frequency, and no distortion is observed at the output of the filter. Output is same as input delayed by some constant.

Expt - 6 Digital Chebyshev Filter Design

In this experiment we had to design Digital Chebyshev using Analog Chebyshev Filter by using Scilab. Chebyshev filters have sharp cutoff characteristics and exhibits ripples in either Pass band or Stop band depending upon the type of filter. Inputs  - Stop band attenuation (As), Pass band attenuation (Ap), Pass band frequency(wp) & Stop band frequency(ws) were taken from the user, same as that of Butterworth Filter, so that comparison can be made between the two

It was observed that magnitude response was equiripple in pass band and monotonic in stop band.Also the order of Chebyshev Filter for same characteristics was small when compared with  Butterworth Filter.The number of valleys and peak in the pass band determined the order of the filter.

Expt - 5 Digital Butterworth Filter Design

This was the first experiment performed in Scilab. Scilab is an open source software designed for doing complex computations using simpler functions.We had to design Butterworth digital filter from from analog Butterworth filter by passing inputs like - Stop band attenuation(As), Pass band attenuation(Ap) , Pass band frequency(wp) & Stop band frequency(ws). Filter order and cut off frequency was then calculated.

 Normalized transfer function of LPF was obtained, which was then converted into denormalized transfer function of desired(LPF or HPF) filter.The response in z -domain is equivalently calculated by IIM or BLT transformations.

 

Frequency Response of Butterworth Filter is maximally flat - monotonically decreasing in Pass band & Stop band. Steepness of the response depends upon order of the filter

Exp - 4. Filtering of Long Data Sequence

For implementing fast processing algorithms like FFT we need all data present at input at the same time. In practical implementation it is not possible to have all data together at same time. Hence it is necessary to decompose the incoming signal into multiple finite length signals to perform operations.  This is done by using - Overlap Add Method (OAM) and Overlap Save Method ( OSM)

In Overlap Add Method x[n] is decomposed into non overlapping sequence of
length L and is performed using Linear Convolution.

In overlap save method, input data sequence x[n] is decomposed into number of
L point sequences, where each data block begins with the last (N-L) values in the previous data block, except the first data block which begins with (N–L) zeros and is performed using Circular Convolution.

Expt. 3 Fast Fourier Transform

The FFT algorithm divides the N-point input signal into 2 parts-even and odd signal values of the input. Computation is carried out only for N/2 signal values, this increases the speed of computations.

The input & output sequence are in a bit reversed manner.

In this lab session we studied and executed FFT of 4 point and 8 point sequence using DITFFT.

We also calculated no. of computations required to find out FFT of a sequence. Comparing it with that of DFT, we can conclude that FFT is much faster.

Expt - 2. Discrete Fourier Transform

Discrete Fourier Transform (DFT) is frequency sampled version  of Discrete Time Fourier Transform (DTFT).It works on the assumption that input is always periodic, to produce periodic results. In this experiment we had to perform  4 point DFT  & 8 point DFT of same input signal.

The magnitude spectrum of both the cases was plotted and compared which helped us draw following conclusion - 
As Length of Input SIgnal (N) increases - 
1. Frequency Spacing increases.
2. Approximation error decreases.
3. Resolution of spectrum increases.

We also calculated the no. of computations required to gt DFT of a signal and concluded that is DFT computationally slow 

Expt - 1. Convolution & Correlation

The aim of the experiment was to study mathematical operations like Convolution and Correlation.
Convolution is the process of computing the output, y[n], of a Linear Time Invariant system to a given arbitrary input x[n] via its impulse response , h[n], summarized in the notation of y[n]=x[n]⋆h[n]:

y[n]=∑k=−∞∞x[k]h[n−k]

It is further classified into two - 
1. Linear Convolution 
    The length of the output signal is N where N=L+M-1 . It is used to determine response of a system when a non - periodic input is applied.

2. Circular Convolution
    The length of the output signal is N=max(L,M). It is used to determine response of a system when a periodic input is applied
(L - Length of input signal i.e x[n] , M - Length of impulse response i.e h[n] ).

Correlation is a process of determining similarity between two input signals.