Assignment 2 Complex Signals and Analysis CSD 9512 Fall 2024 PDF

**Assignment \#2 Complex Signals and Analysis** CSD 9512, Fall 2024 **Due 11:55pm Friday Oct 4 2024 via GradeScope:** This assignment is designed to give you hands-on skills working with sound and its representations (the time waveform, amplitude spectrum, and spectrogram). If you're new to Praat...

**Assignment \#2 Complex Signals and Analysis** CSD 9512, Fall 2024 **Due 11:55pm Friday Oct 4 2024 via GradeScope:** This assignment is designed to give you hands-on skills working with sound and its representations (the time waveform, amplitude spectrum, and spectrogram). If you're new to Praat, don't hesitate to learn with your more experienced classmates, but be sure to turn in your own work. We practiced some of these Praat skills in our Lab \#2 on Thursday Sept 19. See the lab slides and the document "Using Praat for Hearing Science.pdf" for instructions on how to work with Praat for this assignment. Note: When producing spectra, the "Fast" box must be unchecked or Praat takes short-cuts that alter the results! Please number your answers clearly, and provide explanations/reasoning where requested. The required plots can be copied and pasted from the Praat picture window. The numerical results that are requested can be rounded off to the nearest integer value (no decimal places required). It is difficult to read numbers exactly in Praat, so the nearest integer is fine! You will need to download some.wav files from OWL/Brightspace. These are provided in a zip file, Assignment2sounds.zip. [You **must** "unzip" the.wav files into a real folder], otherwise Praat will not be able to load them. **For the questions using Praat formulae, no randomGauss is required... delete that if it shows up!** **Q1.** L~largestLevel\ =\ 85\ db~ L~middleLevel\ =\ 80\ db~ L~smallestLevel\ =\ 70\ dB~ L~smallestLevel~ - L~largestLevel\ =\ -15\ dB~ L~middleLevel~ - L~largestLevel~ = -5 dB L~largestLevel~ - L~largestLevel~ = 0 dB b\) What are the frequencies of the three sinusoids? F~middleLevel\ =\ 300\ Hz~ F~largestLevel\ =\ 600\ Hz~ F~smallestLevel\ =\ 900\ Hz~ F~largestLevel\ =\ 600\ Hz~ Z(t) = 0.5sin(2\*pi\*600\*t) **\ Q2.** A sound is made of a total of five sinusoids. There is the fundamental *f*~0~ (also called the first harmonic), and four more harmonics above that (numbered 2 through 5). Given that the fourth harmonic is 1300 Hz, and the fifth harmonic is 1625 Hz: a. What are the frequencies of the first three harmonics (i.e. the three lowest-frequency tones making up the complex)? H1 = 325 Hz H2 = 650 Hz H3 = 975 Hz H4 = 1300 Hz H5 = 1625 Hz b\) Create this sound in Praat by creating a formula summing five sinusoids \[with no **randomGauss** !\] F1 = 325 Hz θ = 0 Duration = 1.0 s 1. \* sin(2\*pi\*325\*x) + 0.05\* sin(2\*pi\*650\*x) + 0.05\* sin(2\*pi\*975\*x) + 0.05\* sin(2\*pi\*1300\*x) + 0.05\* sin(2\*pi\*1625\*x)  **Q3.** The sensation of beating can be achieved by summing two sinusoids that are close together in frequency, and of similar amplitude. Below is a short chunk of a time waveform showing the sum of two sinusoids of frequencies *f*~1~ and *f*~2~ that are beating: a. What is the beat frequency, or the difference frequency, between the two tones (i.e. *f*~2~-*f*~1~)? Beat freq = 5 Hz The shown image is a combination of two freq. The freq of the shown image cycle/sec is the difference between the two. b\) If the lower frequency sinusoid is *f*~1~=200 Hz, deduce *f*~2,~ then create this sound using a Praat formula. Use amplitude of 0.25 for both tones. Use a start phase θ = 0 for both tones. Make the duration 1.0 s. Listen to the sound. Give the spectrum plot for the frequency range 180 Hz to 230 Hz. You should see the two tones as large spikes. *f*~2\ =~ 200 Hz + 5 Hz = 205 Hz Z(t) = 0.25 \* sin(2\*pi\*200\*x) + 0.25\* sin(2\*pi\*205\*x) c\) Give the spectrum plot for the frequency range 0 Hz to 50 Hz.  No. No, I am not surprised because the given frequencies of 200 Hz and 205 Hz are not in the range of 0 -- 50 Hz. **Q4.** The sound files A2Q4a.wav and A2Q4b.wav both contain a sinusoidal amplitude modulated tone (a SAM tone). They both have the same modulation rate, and they both have the same carrier frequency of *f*~c~=1000 Hz. a\) Load both sounds and listen to them. By inspecting the time plots, what is the modulation rate *f*~m~ ? A2Q4a : 1 cycle/0.1 sec = 10 A2Q4b : 1 cycle/0.1 sec = 10 Both SAM tones have a modulation rate of 10 Hz b\) On different graphs, give the time waveform plot for each sound from t=0 to t=0.2 s. You will not be able to see the individual cycles of the carrier frequency because they are squished together with this relatively large time scale. What you do see is the way the amplitude envelope changes with time (ignore any vertical stripe "artifacts" in the plots).   c\) In a short sentence, describe how the two time waveforms differ in appearance. **Q5.** Give the spectrum plot for the filtered signal over the frequency range 0 Hz to 5000 Hz. 3000 Hz -- 50 Hz = 2950 Hz **Q6.** Each of the plots below (A-F) shows the spectrogram of a different sound.  These questions can be answered by inspecting the spectrograms above. If the answer is not clear by looking at the spectrograms, you can also load the sounds (SoundA.wav... SoundF.wav) into Praat and examine them however you like (time domain, frequency spectra, etc). For each question, explain (briefly!) your reasoning and what methods you used. - **None of these are "trick" questions... just go with the most obvious explanations.** - **Including your explanations for [each] of the six spectrograms in each part is important**. a. Which sounds do not change their basic characteristics over time)? *Explain your decision for each of the six spectrograms*. A does not change their basic characteristics over time. It is a 1000 Hz sinusoid and it does not change over time. I viewed the waveform in Praat and could see that it is continuous and periodic. B does not change its basic characteristics over time. It is a waveform made of harmonics of 500 Hz. It is continuous and periodic C does not change its basic characteristics over time. It is a complex waveform made of multiple frequencies. It is continuous and periodic. E changes its basic characteristics over time. It is noise made of many frequencies. I cannot determine whether the sound is periodic. My analyzing the waveform in praat there is no 'pattern' to be determined from the waveform. It has varying frequency and intensity. D changes it characteristics over time. By listening to the sound, I can tell that it is not constant. By analyzing the waveform (displaying the pitch) I can see that it varies in frequency over time. It has a sharp rise and decay time. F changes its characteristics over time. by listening to the sound, I can tell that it changes over time. by analyzing the waveform, I can see that it is a modulated waveform. There are periods of very low intensity and no pitch. b. Which sounds are periodic in the time domain? *Explain your decisions*. A is periodic. By viewing the waveform I can see it is a 1000 Hz pure tone and it does not change over time. I viewed the waveform in Praat and could see that it is continuous and periodic. B is periodic. It is a waveform made of harmonics of 500 Hz. By viewing the waveform in praat I can see it is continuous and periodic C is periodic. It is a complex waveform made of multiple frequencies. It is continuous and periodic. E is not periodic. It is noise made of multiple frequencies. The frequency varies therefore there is not a constant number of cycles per second. D changes it characteristics over time. By listening to the sound, I can tell that it is not constant. By analyzing the waveform (displaying the pitch) I can see that it varies in frequency over time. F changes its characteristics over time. by listening to the sound, I can tell that it changes over time. by analyzing the waveform, I can see that it is a modulated waveform. There are periods of very low intensity and no pitch. c. Which sounds are frequency-modulated? *Explain your decisions*. What is the modulation rate? D is frequency modulated because frequency is constantly changing, therefore the time it takes for one cycle would change too. Modulation rate = 3 cycles/3 seconds = 1 d. Which sounds are amplitude-modulated. *Explain your decisions*. What is the modulation rate? F is amplitude modulated because there is a difference in intensity. There are some areas where there is energy (black) and some areas where there is not (white spaces). There are changes in the 'darkness'. By analyzing the waveform there are periods of low intensity and no pitch, followed by periods of high intensity and pitch. Modulation rate = 6 cycles/3 seconds = 2 e. For each of the sounds that do not change over time (part a), make a **hand-drawn sketch** (*[not]* a Praat plot) of the amplitude spectrum (i.e. amplitude versus frequency).