FIR filter design using FSM

   
      As in the previous experiment, here too we had to design a digital linear phase FIR filter but using Frequency Sampling Method. In this case, we use the frequency domain analysis where the magnitude and phase of the filter are found from H(k), and then using inverse DFT, h(n) is found.
     The software used was Scilab. Filter parameters like order, cut-off frequency were entered by us and the magnitude spectrum so obtained was used for comparing the stop band and pass band attenuation values with their corresponding calculated values.

FIR Filter Design using Window method

           In this method, an FIR (Finite Impulse Response) filter was designed using a window function. The selection of window depends on the value of stop band attenuation entered by the user. Different window functions like Rectangular window, Hamming window, Hanning window, Blackman window can be used by taking different values of stop band attenuation.
           We designed low pass and high pass linear phase FIR filters and studied the magnitude spectrum of both the filters. The values of Ap and As obtained from the graph were found close to the corresponding calculated values.  

Basic Operations on DSP Processor

             

Basic Operations on DSP Processor

        In this experiment, various basic operations were performed on the DSP processor TMS320F28335. The coding platform used for implementing the operations was Code Composer Studio. The code was written in C language. Operations like addition, subtraction, multiplication, logic operations like AND, OR and shift operations like right shift, left shift were performed.

        Although we performed only these basic operations on the DSP processor, it is capable of performing complex arithmetic calculations like DFT, convolution etc.

DSPP Application (IEEE Paper)

Paper Review

IEEE Paper: Theoretical And Experimental Bases Of A New Method For Separation Of Harmonic And Noise Components Of Speech Signals 

Review:

This paper addresses the problem of separating the noise components from the harmonic components of speech signals describing two traditional methods of improvement of speech signals: first is the period-scaled synchronous analysis of amplitude and phase (which uses Short-Time Fourier Transform for analysis) and second, separation based on a low pass time-filtering of the above parameters. In addition to presenting the theory of the proposed method it also proves through preliminary experiments on synthetic speech, that this method has potential to significantly outperform the reference method based on STFT (Short-Time Fourier Transform). The new theory of noise filtering is called as the H/N (Harmonic-Noise) theory which aims to focus at the period scale. This method is both time and frequency domain as it refers to the Fourier series expansion of each signal period instead of the usual STFT approach. The experimental result gives typical signal to error ratio gains of 5dB. Apart from this, the paper also discusses conditions which can bring this practical value of gain closer to the theoretical value.    

DSPP Application (Patent)

Patent Review

United States Patent US005142164A:  SUBHARMONIC NOISE REDUCTION CIRCUIT

Patent No.: 5,142,164

Inventor: Federico Chu, Des Plaines, Ill.

Review:

                The patent provides a sub-harmonic noise reduction circuit that reduces the signal-to-noise ratio of an electrical circuit having inherent sub harmonic distortion. The invention uses a 2-stage electronic circuit: first stage being a low pass filter and the second, a differential amplifier. The objective of this invention is to provide a sub-harmonic noise reduction circuit that operates with an extended life and relatively low drift when subjected to temperature, humidity or other environmental changes. The circuit is therefore designed to give a reliable DC level output voltage for a given input regardless of the AC distortion which is seen from the graphs. A conventional noise reduction technique requires the use of Fourier Transform which leads to a relatively expensive hardware and/or software as well as excessive power compared to the amplifier circuit of this invention which does not use any complex analysis or hardware, instead using simple time domain analysis.

Digital Chebyshev Filter Design

                

               This filter design is similar to the previous Butterworth filter design. The parameters entered for Chebyshev low pass and high pass filters were also the same (pass band and stop band attenuation, pass band and stop band digital frequencies, sampling frequency). Scilab was used here too for the design implementation where the parameters were entered in the Console window when the program is to be executed and the magnitude spectrum of the filters was seen on the graphic window. As in case of Butterworth Filter, we kept the difference in the two frequencies more in order to get accurate results. Also, the sampling frequency can be kept as more than twice or thrice the maximum frequency.  It is observed that in low pass and high pass Chebyshev filters there is a ripple in the pass band and no ripple in the stop band.

Digital Butterworth Filter Design

                  In this experiment, digital Butterworth low pass and high pass filters have been designed using Scilab software. Scilab is a free and open source software for numerical computation where one can use the source code and modify it according to the requirement of the project or research for personal or commercial use. We implemented low pass and high pass filter where we had to enter the pass band and stop band attenuation, pass band and stop band digital frequencies and the sampling frequency. Ideally the observed stop band attenuation should be greater than the calculated while the pass band attenuation should be lesser than the calculated one. However it was seen that if the difference in the pass band and stop band frequencies was less, then the above values were not close to the calculated ones. Hence we increased the gap between the two frequencies which got us the accurate results.

OAM and OSM

           OAM (Overlap Add method) and OSM (Overlap Save Method) were the two methods (implemented in C) that we used to find the output of FIR filter.

           

           The value of N we selected was 8 and L was 5. Hence in OAM, the 13-pt sequence that we entered got decomposed into 3 parts and convolution of each part was calculated using FFT algorithm.

           Similarly, in OSM too the sequence was decomposed into 3 parts and circular convolution is found after which the overlapped part is neglected and the rest becomes the output.

FFT

DSPP Practicals

         FFT (Fast Fourier Transform) has less no. of computations (real and complex addition and multiplication) than DFT, hence it was implemented. 

         There are two types of FFT viz. DIT-FFT (Decimation In Time FFT) and DIF-FFT (Decimation In Frequency FFT) out of which we implemented DIT-FFT using C.

The input signal we used for computing FFT was the same as that used in DFT. It was seen that the output in both the cases was same which proves that DFT and FFT produce same results. 

DFT

DSPP Practicals

         DFT (Discrete Fourier Transform) is basically the sampled version of DTFT (Discrete Time Fourier Transform) signal.

         Depending upon the maximum length of input signal mentioned in the code, an input sequence of length=4 was entered. However if 8-point sequence was entered with the last four values as zero, then the resolution and accuracy increases i.e. between every 2 values of 4-pt DFT output, a new value got added.

         It was seen from the code that DFT requires a number of real and complex additions and multiplications. Hence processing of a signal using DFT takes longer time.

Convolution and Correlation

DSPP Practicals

           Convolution is used to find the output of a given discrete time signal.

           In linear convolution, if the length of input signal is L and  that of impulse reponse is M then length of output signal should be equal to L+M-1. In our code, if the length was exceeding the length given by the above formula, then the last extra values were getting added to the first corresponding values and this is termed as aliasing.

           In circular convolution the length of the output signal is taken as the maximum of the length of the two input signals. This type of convolution hence uses the method of zero padding.

           Correlation is used to find the degree of similarity between the two input signals.

           Auto-correlation is correlation of two same signals. Hence it is seen that the auto-correalation output is an even signal. Cross-correlation of the input signal and its delayed signal gives a shifted/delayed output signal.