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Step 2: In a filter bank analysis, an input signal is fed into a series of analysis filters (in this project we use N = 128 filters), decomposing the signal into subbands. Low Frequency filter (LF) Analysis filter H (2) pi[n] Synthesis filter 91 [n] G (2) x[n] Pm[n] am[n] [n] Analysis filter Hm(z) Synthesis filter Gm(z) + This means that the output signal from each analysis filter represents different frequency components of the input signal. The analysis filters Hm(z) (see Figure on the right) comprise a set of overlapping N bandpass filters used to model the human auditory filters as explained in the previous slides. The synthesis filter Gm(2), in each channel employs the time reversed impulse response of the analysis filter, Hm(2). The analysis filter Hm(z) (impulse response h[n]) can be implemented in practice as an FIR filter. By time reversing the FIR analysis filters' impulse responses, we can form the synthesis filters (Impulse response h[-n]} and an overall zero phase characteristic is obtained. Perfect reconstruction of the input signal x[n] is achieved if and only if the output signal [n] is identical to x[n] or a delayed version of x[n]. Show that perfect reconstruction is possible if EM=1 Gm (z) Hm (z) = K where K is appositive constant. Pn[n] Analysis filter Hn(z) Synthesis filter GN(z) an[n] High Frequency filter (HF) Block Diagram of Analysis/Synthesis Filter Bank Step 2: In a filter bank analysis, an input signal is fed into a series of analysis filters (in this project we use N = 128 filters), decomposing the signal into subbands. Low Frequency filter (LF) Analysis filter H (2) pi[n] Synthesis filter 91 [n] G (2) x[n] Pm[n] am[n] [n] Analysis filter Hm(z) Synthesis filter Gm(z) + This means that the output signal from each analysis filter represents different frequency components of the input signal. The analysis filters Hm(z) (see Figure on the right) comprise a set of overlapping N bandpass filters used to model the human auditory filters as explained in the previous slides. The synthesis filter Gm(2), in each channel employs the time reversed impulse response of the analysis filter, Hm(2). The analysis filter Hm(z) (impulse response h[n]) can be implemented in practice as an FIR filter. By time reversing the FIR analysis filters' impulse responses, we can form the synthesis filters (Impulse response h[-n]} and an overall zero phase characteristic is obtained. Perfect reconstruction of the input signal x[n] is achieved if and only if the output signal [n] is identical to x[n] or a delayed version of x[n]. Show that perfect reconstruction is possible if EM=1 Gm (z) Hm (z) = K where K is appositive constant. Pn[n] Analysis filter Hn(z) Synthesis filter GN(z) an[n] High Frequency filter (HF) Block Diagram of Analysis/Synthesis Filter Bank

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