FFT and signal processing.

 

Using this function try to process various signals and answer the following questions:

1. Find the error in function. Hint: add a constant component to the signal.

2. Why are the spectral amplitudes not exactly equal to the component amplitudes? How to improve the match?

3. Try to process the signals with different sampling periods and signals of different duration.
What changes in the obtained spectra can you mention? How can you explain the observed effects?

4. Try to put two frequencies close in the original signals (but not too close). What do you observe?
When the frequencies are resolved in the spectrum, and when are they not?
Also, try to variate the amplitudes (ratio of amplitudes) of these two close components (harmonics) along with their frequencies.
Which methods of handling such signals can you proposed? Namely, how is it possible to resolve the close frequencies?

To resolve these tasks, try to implement several options:
a) increase n (i.e. pad the original signal with zeros);
b) consider gga function from ltfat package;
c) use window functions. Decide which one is the most suitable?

Sample Solution

and interaction between Native people and European empires within that physical or ideological space.

In Richard White’s novel, he describes the “Middle Ground” as two different and distinct concepts. The first of these concepts is a then French region of North America which consists of parts of Michigan, Wisconsin, and Canada, among others. The second definition was a process of mutual appeasement and accommodation between the Native American tribes of the region and the French, British, or Americans that they were negotiating with. This term refutes the myth that Europeans, from the minute they stepped foot on the American continent, had the upper hand. Richard White’s concept of the “Middle Ground” is proven correct based on the gift-giving relationship between the Indian and mainly French settlers.

One aspect of Indian and European relationships that represents the “Middle Ground” is gift-giving. These gift exchanges “lay at the heart of Indian relations with other Indians, and they became equally important in Indian relations with the Spanish, French, and English,” (Calloway, p.139). When they first came to the United States, Europeans had to learn these customs in fear of being seen as rude. These exchanges “were not conducted solely for profit but involved social, political, and even spiritual aspects as well as economic incentives,” (Calloway, p.140). It was important to maintain this relationship with the Indians because “France’s North American empire…depended on the maintaining the goodwill of an array of Indian peoples,” (Calloway, p.140).

While this gift giving relationship between the Native Americans and the mainly French settlers helped the trading of goods between the two sides for a while, this all changed after

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