Tasks to do:

• Linear convolution
  • Create the first sequence representing the impulse response h[n] of moving-average (MA) filter of the order M=100, i.e. the length of resulting impulse response should be N1=M+1=101 samples.
  • Create the second sequence of the length N2=4000 which represents the input signal x[n] containing the addition of sinusoid with zeros phase shift and parameters A = 1, f = 12 Hz, fs = 8000 Hz and white noise with normal distribution, mean value 0 and variance equal to 1.
  • Realize the suppression of white noise on the basis of the linear convolution (fcn conv) using the above mentioned MA filter.
  • Result: Display
    • created impulse response h[n] of MA filter,
    • frequency response of MA filter with impulse response h[n],
    • generated input signal x[n],
    • filtered output signal y[n], i.e. the result of linear convolution of signals x[n] and h[n].

  • IN THE FREE TIME or as HOMEWORK:
    Repeat steps mentioned above using the filter with exponential averaging with the impulse response of the length N1=101 samples, described by the formula h[n] = 0.02 * 0.98^n. Discuss also a possibility of realization such a filtering by IIR filter.

• Cyclic convolution
  • Compute cyclic convolution between sequences x[n] and h[n] using DFT of the order:
    - NDFT = N2,
    - NDFT = N1+N2-1
    - NDFT = N1,
    - NDFT > N1+N2-1.
  • Compare obtained results for linear and cyclic convolution in one figure and explain differences.

• Realization of cyclic convolution for long signals (on-line processing)
  • Realize the filtering on the basis of cyclic convolution using independent processing in particular short-time frames of the length NFFT = 512 samples. Realize the segmentation without overlapping and compare results obtained by linear and cyclic convolution.

  • Overlap-And-Save (OLS) and Overlap-And-Add (OLA) for short-time realization of cyclic convolution
    Realize the filtering based on cyclic convolution in short-time frames using the OLS and OLA technique (Overlap-And-Save and Overlap-And-Add). Choose in both cases FFT order NFFT = 512 samples and compare the results obtained by linear and cyclic convolution using OLS as well OLA technique.

  • Result:
    • Display and compare output signals computed on the basis of linear and cyclic convolution usign OLS and OLA.

• Modeling of reverberations in long acoustic signal
  • On the basis of any technique from above mentioned ones (i.e. OLS or OLA) realize the filtering which models an echo in signal collected in the room with higher reverberations. Below linked wav-signals can be loaded into MATLAB environment using the function audioread, for the purpose of further listening, save also the information about sampling frequency during the loading of data into MATLAB environment.
  • Result:
    • For measured impulse response ir_iim03.wav (possibly shortened) and input signal guitar_dry.wav display a compare modelled reverberated signals computed on the basis of:
      - linear convolution,
      - short-time cyclic convolution using OLS or OLA
      - short-time cyclic convolution without overlapping,
      - listen obtained results.
    • Compare also the computer time needed for the computation of linear and cyclic convolution.

  • Repeat the processing also for the following signals:
    - impulse responses: ir_iim01.wav, ir_iim02.wav, ir_betlem.wav,
    - processed signal: voice_dry.wav