<p>The main issue in this thesis is to minimize the number of operations and the energy consumption per operation for the computation (arithmetic operation) part of DSP circuits, such as Finite Impulse Response Filters (FIR), Discrete Cosine Transform (DCT), and Discrete Fourier Transform (DFT) etc. More specific, the focus is on the elimination of most frequent common sub-expression (CSE) in binary, Canonic Sign Digit (CSD), Twos Complement or Sign Digit representation of the coefficients of non-recursive multiple input multiple output (MIMO)  FIR system , which can be realized using shift-and-add based operations only. The possibilities to reduce the complexity i.e. the chip area, and the energy consumption have been investigated.</p><p>We have proposed an algorithm which finds the most common sub expression in the binary/CSD/Twos Complement/Sign Digit representation of coefficients of non-recursive MIMO multiplier less FIR systems. We have implemented the algorithm in MATLAB. Also we have proposed different tie-breakers for the selection of most frequent common sub-expression, which will affect the complexity (Area and Power consumption) of the overall system. One choice (tie breaker) is to select the pattern (if there is a tie for the most frequent pattern) which will result in minimum number of delay elements and hence the area of the overall system will be reduced. Another tie-breaker is to choose the pattern which will result in minimum adder depth (the number of cascaded adders). Minimum adder depth will result in least number of glitches which is the main factor for the power consumption in MIMO multiplier less FIR systems. Switching activity will be increased when glitches are propagated to subsequent adders (which occur if adder depth is high). As the power consumption is proportional to the switching activity (glitches) hence we will use the sub-expression which will result in lowest adder depth for the overall system.</p>

The main issue in this thesis is to minimize the number of operations and the energy consumption per operation for the computation (arithmetic operation) part of DSP circuits, such as Finite Impulse Response Filters (FIR), Discrete Cosine Transform (DCT), and Discrete Fourier Transform (DFT) etc. More specific, the focus is on the elimination of most frequent common sub-expression (CSE) in binary, Canonic Sign Digit (CSD), Twos Complement or Sign Digit representation of the coefficients of non-recursive multiple input multiple output (MIMO)  FIR system , which can be realized using shift-and-add based operations only. The possibilities to reduce the complexity i.e. the chip area, and the energy consumption have been investigated. We have proposed an algorithm which finds the most common sub expression in the binary/CSD/Twos Complement/Sign Digit representation of coefficients of non-recursive MIMO multiplier less FIR systems. We have implemented the algorithm in MATLAB. Also we have proposed different tie-breakers for the selection of most frequent common sub-expression, which will affect the complexity (Area and Power consumption) of the overall system. One choice (tie breaker) is to select the pattern (if there is a tie for the most frequent pattern) which will result in minimum number of delay elements and hence the area of the overall system will be reduced. Another tie-breaker is to choose the pattern which will result in minimum adder depth (the number of cascaded adders). Minimum adder depth will result in least number of glitches which is the main factor for the power consumption in MIMO multiplier less FIR systems. Switching activity will be increased when glitches are propagated to subsequent adders (which occur if adder depth is high). As the power consumption is proportional to the switching activity (glitches) hence we will use the sub-expression which will result in lowest adder depth for the overall system.