Basic properties of periodogram and application examples

**Tasks to do: **

**DFT - periodogram, spectral leackage**- Generate sinosoid with parameters
*f=1000 Hz, fs=8000 Hz, to=0.1 s*(duration). - Choose the short-time frame with the length of
*N=512 samples*and compute its periodogram using DFT (fcn). Describe correctly scale on frequency axis in Hertz and observe various way of results displaing (i.e. use fcn**fft**with varoius parameters or fcn**plot**).**stem** - Observe also the periodogram for frame length of
*N=512, 510, 508 samples*and*N=512, 515, 520 samples*. Explain observed results for varying frame length. - Repeat poit above for sinosoid with parameters
*f=1231 Hz, fs=8000 Hz, to=0.1 s*(duration) for frame length of*N=512, 510, 508 samples*. Explain a difference in comparison to the previous case of the sinusoid with*f=1000 Hz*. - Repeat the same analyses when Hamming window is used for
short-time frame weighting (fcn
).**hamming** - Observe
**short-time DFT spectrum of speech signal**. - 1st checked result:
Read the part of voiced speech sound vm4.bin, which is sampled
by
*fs = 16 kHz*and saved in raw binary form without a header. To load it into MATLAB environment use attached function loadbin.m, this function is not part of any standard MATLAB toolbox! You should place it into your working directory! Realize the following analyses for given signal:- draw short-time power spectrum in dB for the first available
frame with the length of
*N=512*samples, - compare the spectrum for weighted (Hamming window) and unweighted (rectangular window) short-time frame,
- determine the frequency of the first main peak in spectral envelope,
- compare power spectra computed for the frame lengths of
*N=64, 128, 256, 512, 1024, 2000*samples.

- draw short-time power spectrum in dB for the first available
frame with the length of
- In the case of free time, repeat illustratively also for signals: vf0.bin, vm0.bin, vf1.bin, vm1.bin, vf2.bin, vm2.bin, vf3.bin, vm3.bin, vf4.bin, vm4.bin, vf5.bin, vm5.bin, vf6.bin, vm6.bin, vf7.bin, vm7.bin, vf8.bin, vm8.bin, vf9.bin, vm9.bin.

- Generate sinosoid with parameters
**Zero padding in computation of DFT**- Generate the sinusoid with
*f = 1231 Hz*,*fs = 8000 Hz*nad the frame length of*N=512*samples. Observe periodogram computed by DFT with the order of*NDFT = 512, 1024, 2048, 4096, 8192*and explain obtained results. - Accuracy improvement for the analysis of harmonic components in a record.
- 2nd checked result:
Load signals sig1.mat and
sig2.mat containing the short records
of a mixture of harmonic components with background gaussian white noise. The
signals are sampled by
*fs = 200 Hz*and they are saved in MATLAB binary format. Use the fcn*load*to load the data into MATLAB. Determine for both signals:- number of harmonic components and their frequencies,
- do it on the basis of DFT spectrum computed from available length
of
*N=40*samples or from the record extended by zeros to the length of*N=512*samples.

- Generate the sinusoid with
**Periodicity in Short-Time DFT Spectrum**- bserve periodograms of following signals which contain one, two, three, or four periods of voiced speech sound vm0-1-per.bin, vm0-2-per.bin, vm0-3-per.bin, vm0-4-per.bin. The signals have binary format, to load them into MATLAB use the function loadbin.m. and find shor-time DFT of these signal. Length of the DFT should be always the same as length of analyzed signal.
- Observe the changes in the spectrum of the signal vm0-4-per.bin (with 4 periods) when
it is analyzed by DFT of the order

a) 479, 481

b) 470, 490

c) 256, 512

d) 1024

e) 2048 - 3rd checked result:
Observe the priodicity in the real signal (part of voiced phone) vm0-real-per.bin and try to estimate
fundamental period (and fundamental frequency) of given
quasiperiodic signal (voiced speech sound). Compute the periodogram for

a) NFFT = 512

b) NFFT = 4096 - 4th checked result:
Observe the spectrum on aperiodic signal (part of unvoiced phone) real-non-per.bin and compare for srovnejte s
předchozíprevious variant of periodic signal. Compute the priodogram
again for

a) NFFT = 512

b) NFFT = 4096IN THE CASE OF FREE TIME

- Determine the voice pitch also for other records referenced in the
first item of this exercise.
- Determine the pitch of musical instrument tones from last week exercises and compare it with the results achieved using autocorrelation analysis - cembalo_d_dur_2.wav, fletna_d_dur_6.wav, housle_d_dur_5.wav, kytara_d_dur_1.wav, piano_d_dur_4.wav, varhany1_d_dur_3.wav, varhany2_d_dur_8.wav.