QUESTION

Text
Image

1. Write a Matlab function x = sym2TT(S) that generates a 100 milliseconds time-domain signal corresponding to a given DTMF symbol S. The set of all DTMF symbols and their corresponding frequencies are indicated in Figure 1.

2. Generate a signal xptq which contain a sequence of DTMF symbols corresponding to your cell phone number. Add a 20 milliseconds guard interval between consecutive DTMF symbols. 3. Create a signal yptq which is the signal xptq contaminated with additive white Gaussian noise with variance 0.1.

4. Store the generated signal yptq as an audio file with extension (*.wav)

5. Plot the signal yptq. Note that, this plot does not provide any frequency-domain information about yptq.

6. Use the FFT command to obtain the spectrum Y pfq of the signal yptq, hence plot the magnitude spectrum (in dB) in the frequency range 600Hz ¤ f ¤ 1700Hz. Note that, this plot does not provide any time-domain information about yptq

. 7. Matlab code to create a set of spectrograms of the signal yptq using the following parameters: Overlap between the sliding windows: 50% FFT size: 214, this is the total number of samples in time-domain and in frequency-domain as well. Time-domain window size: use the following values t16, 64, 256, 1024, 4096u.

Create a spectrogram for each window size (t16, 64, 256, 1024, 4096u) using a rectangular time-domain window.
Figure 1: Dual-Tone Multi-Frequency (DTMF) Signalling Scheme

Which window size provides a ”kind-of” optimal trade-off between time and frequency resolutions? Change the time-domain window to a blackman window and create a spectrogram for each window size (t16, 64, 256, 1024, 4096u). For a given window size, which window type (rectangular or blackman) provides a better frequency resolution ? Write Matlab code to decode the signal yptq, verify that you will obtain your cell phone number.

Public Answer

11SQGS The First Answerer