Basic Operations using DSP processor

We were taught the basic arithmethic and logical operations using the procedure of how to program a DSP processor and we saw various arithmethic and logical syntaxes. We learnt addition, subtraction , multiplication , division and logical shift left,right etc. 

Digital FIR filter design using windowing method

In this experiment we had to design a digital filter using windowing technique and study the spectrum of the filter .We learnt that in the magnitude response of the FIR  filter there we ripples present in the stopband of LPF.  For BPF and LPF  the phase response is linear and the values of Ap and As almost match according to the window used by us.  

Digital FIR filter design using frequency sampling method (FSM)

From this experiment we learnt that phase response will be the same for LPF and HPF depending on whether the orders are kept same . Also the values of Ap and As have been verified . 5 parameters namely attenuation in both pass band and stop band in dB, pass band and stop band frequency in Hz and sampling frequency in Hz were taken from the user.

Digital Chebyshev Filter Design

In this experiment we had to design a Digital Chebyshev Filter from Analog Chebyshev Filter BLT.

From the experiment we learnt that for an LP Digital Chebyshev Filter the ripples are present in the passband whereas the stopband is monotonic and vice versa for HP Digital Chebyshev Filter. Also in both the high pass and low pass filter, poles are present inside the unit circle , hence they are stable. For LPF there is definite zero at z=-1 while for HPF there is a definite zero at z=1.

The values of Ap and As as i/ps are tallied.

Digital Butterworth filter

In this experiment we had to design a digital filter from analog filter and study the aliasing effect due to sampling in Impulse Invariant Method and the frequency warping effect in BLT method .

So after obtaining the results we learn that analog LPF poles lie on the LHS  of the s- plane and digial LPF  poles lie inside the unit circle . Hence both analog and digital butterworth LPF are stable . 

Patent Review:Audio signal extraction and Correlation

Patent Publication No:US 20050232411 A1.

Audio signature extraction, basically describes a method to detect a specific program or channel on basis of a unique key signature. This is used in television sets to identify various channel. The signature can be sent with data or when frame transmission is offline. The easiest method to implement this is using correlation. An incoming time domain moment can be captured and correlated with a stored reference signal to identify whether it belongs to a specific channel or not. 

This patent includes 50 claims which include the methods of deriving the signal by segregating them into blocks and finding their spectral moments. At least one of these spectral moments is then converted into the signature.

IEEE paper review: Design of Audio Signal Processing and Display System Based on SoC

In this paper, the authors have realised an efficient way of  audio processing by using the functionalities of a designed system on chip. They have used a Xilinx-sync 7000 development platform for the same.

In the market survey before this paper there was only the existence of audio processing techniques divided into two parts namely-Firstly, audio data acquisition and playback based on ARM and Secondly audio data acquisition using DSP or FPGA. ARM has good control but is slow and not good for signal processing whereas FPGA is fast and has parallel processing capabilities and is fast but has very less control.

Hence a system on chip with both features for real time data processing.The system takes in an external input and then at the output we receive rock, pop, classical etc types of music. The ARM part is responsible for control of software and FPGA processes the audio data.

This processed audio data is segregated into different frequency segments and after their gain processing we get different types of music. Hence this hardware software combination on one chip implements clear efficient audio processing techniques.

Link: http://ieeexplore.ieee.org/document/7490868/. 

Overalp ADD and Overlap SAVE.

Whenever we come across larger sequences that are required to be processed, say a large valued sequence is given to a digital FIR filter, Overlap add method or Overlap save method is used, where faster processing of the signals is needed.

This can be either done by overlapping values after decomposing the input, adding zeros to make it equivalent to L (where L=N-M+1) and linear convolution of these decomposed inputs with h(n) ie OAM

or by decomposing the input, adding preceding values to each of the decomposed input to make it equivalent to L, circular convolution with h(n) and then eliminating padded number of values from each convoluted output to obtain the final output. ie OSM.

OAM and OSM are block processing techniques as seen above and computationally occupy similar memory space.

Fast Fourier Transform

FFT is a faster computational method compared to DFT as the signal is divided into even and odd parts and computations for both are done alongside. We see that the first value is always the sum of input signal values. 

We have taken two sequences 4pt and 8 pt. and found their Fast Fourier Transforms to study these radix 2 FFT algorithms. The computation is carried out only for N/2 values and makes it the fastest algorithm computationally.

 

 

Discrete fourier transform

In this experiment we have verified the Discrete Fourier Transform of a signal by executing a C- program for the same wherein arrays have been used to store real and imaginary parts of the signal.
This signal is manipulated (such as zero padded or expanded form of the same signal) in different ways through this experiment and for each situation we have studied the result.

DFT is the frequency sampled version of DTFT hence giving periodic results.
We also plot its magnitude spectrum by approximation for both 4pt and 8pt (zeros appended to 4pt sequence) signals as well as expanded signal by adding zeros between the for 4pt sequence.
We observe that expansion in time domain gives a compressed spectrum in frequency domain and by finding number of additions and multiplications required we concluded that DFT is computationally slow.

Discrete Convolution and Correlation

Through this experiment, we have aimed to comprehend the Convolution and Correlation of Discrete signals by programming for the same in C-language and tallying them with their mathematically verified outputs.
Results obtained for the following were analyzed to derive legitimate conclusions:
1. Linear Convolution
2. Circular Convolution
3. Linear using Circular Convolution
4. Auto-correlation
5. Cross-correlation
In convolution, we have taken varied lengths of the two input signals to get different results for linear and circular convolution and have observed an aliasing effect in circular convolution. 
In Correlation, we have found auto-correlation and cross-correlation in combinations of original, delayed and scaled values of the same signal in order to find degree of similarity between two signals.