• Study the principle of filter-bank-based decomposition and back synthesis of a signal into frequency bands. Use the following script example_filter_banks_proto.m and signal s0001.bin (fs = 8 kHz, raw, 16-bit PCM, to load into MATLAB use function loadbin.m) which represents a brief summary of seminar done within the subject BE2M31DSPA. Observe signals in particular steps, study mainly the impact of decimation and interpolation in particular subbands.
• Observe the power of error signal at the output of synthesis filter bank.
• Observe the change of error signal level for the case of a prototype designed in MATLAB using function fir1 and for the case of a optimum prototype designed on the basis of perfect reconstruction. Coefficients of this prototype are available in the referred script.
• Result:
  • Comparison of analysis and synthesis into 2 bands for above given filter bank.

THE FIRST WEEK - HOMEWORK :

• Realize the decomposition into more frequency bands and further the back synthesis as well which is based on Quadrature Mirror Filter Bank (QMFB). Use as the basis for recursive decomposition/synthesis the above mentioned solution for 2 bands. Implement this decomposition using general number N of filter-bank stages.
• Organize input and output signals for each particular sections within matrices, where signals in particular bands are organized in columns of these matrices.
• Determine the delay of signals generated by used filter bank with N stages and compensate it in the end.
• Determine error signal between the input signal and the output of used filter bank and compute signal-to-noise ratio according to the formula SNR_e = 10*log10(Ps/Pe).
• Use the following signals:
  - SA001S01.CS0 (fs = 16 kHz, raw data, 16-bit PCM, to load it into MATLAB use function loadbin.m),
  - or other speech or acoustic signal (it is possible to use your own record of an utterance),
  - ideal unit pulse at the position 2500 of total signal length 10000 samples.
• Result :
  • Display original signal, signals decomposed into particular bands of used FB.
  • Display signal at the output of synthesized filter bank and related error signal.
  • Determine achieved SNR_e for decomposition/synthesis with MATLAB-based or optimum prototype respectively.
• CLASSIFIED HOMEWORK (4 points):
  • Deliver the solution via WEB interface at MOODLE FEE, see HOMEWORK - WAWELETS.

THE SECOND WEEK :

• Realize wavelet-based noise suppression in band signals decomposed using QMFB (Quadrature Mirror Filter Bank). Suppress the noise on the bsis of hard or soft thresholding, determine the suitable level of threshold on the bases of noise-only part of processed signal.
• Work with chosen speech or acoustic signal with additive white Gaussain noise of zero mean values and varying level, i.e. observe the case with lower or higher level of noisy background.
• Analyze also results for the case color background noise. You can use the following color noises:
  - nc1.bin (to load signal into MATLAB use function loadbin.m) - low-frequency artificial noise,
  - nc2.bin - high-frequency artificial noise,
  - nc3.bin - band artificial noise,
  - nc4.bin - band artificial noise.
• Result :
  • Display original noisy signal, signals decomposed in particular bands before and after thresholding, back-synthesized signal with suppressed noise background.
  • Compare input signal-to-noise ratio SNR_in of noisy signal and achieved SNR_out of output enhanced signal with suppressed noise.