The problems are from Fourier Series, Fourier Integral, and Fourier Transform. Please show each step of your solution.

Obtain a computer plot of the partial sums of the Fourier series (19) of the periodic function shown in the attached figure, for
(a) n =2
(b) n = 5
(c) n = 10
(d) n = 20
(e) n = 30
(f) n = 50

Please view the attachment for the rest of the question.

This solution shows how to calculate the partial sums of a Fourier series of a given periodic function. The solution is provided within an attached pdf. file.

... n} (where n does not equal zero in the sum) is the ... Show that the Fourier series is convergent ... by which we mean, as usual, that the symmetric partial sums of the ...

... We can compute this integral by partial integration, the integral of the ... The Fourier series for f(x) is thus: f(x) = R[ pi/4 + sum from n = 1 to infinity of J_1 ...

... excel, draw a plot of the partial sum of the Fourier series which uses just there first four non-zero terms and comment on it in relation to your plot (i). ...

... We write the function we want to sum f (x) in terms of it's Fourier transform f (k ): ∞ f (x) = f (k ... When we sum the terms, the partial summation seems ...

Partial diff equation. ... of p I use n since in most text books n is the more common index for Fourier series. ... But, integration of a sum is like summing integrals. ...

... I am using separation of variables and Fourier Series as the ... into the original equation, the partial derivatives become ... put the term inside the sum: (1.29) Now ...

... and explain how you would obtain i ts Fourier series, develop the ... we can split this fraction into partial fractions with ... This can be written as a sum of known ...

... 11 By doing partial derivatives and introducing in (Eq.10 ... the solution can be written a an infinite sum of all ... to expand a function in a Fourier series, in our ...

... the and for a combination of partial pressures of ... part and the magnitude of the Fourier transform of ... XDAP; dotted line, residuals remaining when the sum of the ...

... R4b) ide with Cl atoms in air using Fourier transform in ... At room temperature and an oxygen O partial pressure of ... The sum of the yields of AFAN and formic acid ...