Answer Happy

The short-time Fourier transform (STFT) is often used for computing the spectrogram of an audio signal. Assume that the audio signal is sampled at F kHz, and the windows of A samples are used for computing the spectrogram, with 8% overlap between two neighbouring windows. With the values of the parameters given in Table 1, answer the following questions. (0) Explain why STFT is used for analysing an audio signal rather than the standard discrete Fourier transform (DFT). What advantage is gained by using STFT over DFT? [Provide your answer in about 100 words) (10 %) (i) Calculate the hop size (in samples), and the time and frequency resolution of the spectrogram. Explain how you obtain the answer. [20% ] (1) (i), what If the frequency resolution is increased to M times as high as in should be the window length? Explain how you obtain the answer. [10 %] (iv) If the overlap between the two neighbouring windows is changed to C%, what should be the hop size? Explain how you obtain the answer. [10 %] (v) Suggest a method that can mitigate the problem of spectral leakage when mputing STFT and provide reasoning for your method. [10 %] [TO CONTINUE ON NEXT PAGE] 2 EEE3042/7/SEMR2/21/22 (1 hand-out) Second rightmost digit of student number (URN) A B C F 0 1024 30 60 18 1 512 20 60 10 2 1024 30 60 18 3 512 20 60 10 3 4 2048 40 50 8 3 5 1024 30 60 18 2 6 2048 50 75 8 3 7 1024 30 60 18 2 8 2048 40 50 8 3 9 512 20 60 10 3 Table 1 The values of the parameters specified with respect to your student number (URN). Example: if your URN is "6789042", the second rightmost digit is "4", so you will use: A-2048, 8-40, C-50, F-8, M-3. M 2 3 2