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edited Jul 3, 2018 at 20:46

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I'd like to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. Here is something that I attempted.

 s[n_, x_] :=  8/4 + 3/(9 \[Pi]π) Sum[(6 (-1)^k)/(k \[Pi]π) 
                Cos[(k \[Pi]π x)/2] + (16 (-1)^k + 13)/(\[Pi]π k) 
                Sin[(k \[Pi]π x)/2],{k, 0, n}]

 partialsums = Table[s[n, x], {n, 1, 5}];

 f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}]

 Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

Any ideas about the best method to tackle something like this?

I'd like to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. Here is something that I attempted.

 s[n_, x_] :=  8/4 + 3/(9 \[Pi]) Sum[(6 (-1)^k)/(k \[Pi]) 
                Cos[(k \[Pi] x)/2] + (16 (-1)^k + 13)/(\[Pi] k) 
                Sin[(k \[Pi] x)/2],{k, 0, n}]

 partialsums = Table[s[n, x], {n, 1, 5}];

 f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}]

 Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

Any ideas about the best method to tackle something like this?

I'd like to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. Here is something that I attempted.

 s[n_, x_] :=  8/4 + 3/(9 π) Sum[(6 (-1)^k)/(k π) 
                Cos[(k π x)/2] + (16 (-1)^k + 13)/(π k) 
                Sin[(k π x)/2],{k, 0, n}]

 partialsums = Table[s[n, x], {n, 1, 5}];

 f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}]

 Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

Any ideas about the best method to tackle something like this?

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occurred Mar 3, 2012 at 0:02

deleted 6 characters in body

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edited Mar 2, 2012 at 23:41

Sjoerd C. de Vries

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I am wantingI'd like to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. Here is something that I attempted.

s[n_, x_] :=  8/4 + 3/(9 \[Pi]) Sum[(6 (-1)^k)/(k \[Pi])

 s[n_, x_] :=  8/4 + 3/(9 \[Pi]) Sum[(6 (-1)^k)/(k \[Pi]) 
                Cos[(k \[Pi] x)/2] + (16 (-1)^k + 13)/(\[Pi] k) 
                Sin[(k \[Pi] x)/2],{k, 0, n}]

 partialsums = Table[s[n, x], {n, 1, 5}];

 f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}] 

 Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

partialsums = Table[s[n, x], {n, 1, 5}];

f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}]

Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

Any ideas ofabout the best method to tackle something like this.?

I am wanting to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. Here is something that I attempted.

s[n_, x_] :=  8/4 + 3/(9 \[Pi]) Sum[(6 (-1)^k)/(k \[Pi])

                Cos[(k \[Pi] x)/2] + (16 (-1)^k + 13)/(\[Pi] k) 
                Sin[(k \[Pi] x)/2],{k, 0, n}]

partialsums = Table[s[n, x], {n, 1, 5}];

f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}]

Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

Any ideas of the best method to tackle something like this.

I'd like to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. Here is something that I attempted.

 s[n_, x_] :=  8/4 + 3/(9 \[Pi]) Sum[(6 (-1)^k)/(k \[Pi]) 
                Cos[(k \[Pi] x)/2] + (16 (-1)^k + 13)/(\[Pi] k) 
                Sin[(k \[Pi] x)/2],{k, 0, n}]

 partialsums = Table[s[n, x], {n, 1, 5}];

 f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}] 

 Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

Any ideas about the best method to tackle something like this?

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asked Mar 2, 2012 at 18:44

night owl

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3
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Plotting Partial Sums of Fourier Series

I am wanting to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. Here is something that I attempted.

s[n_, x_] :=  8/4 + 3/(9 \[Pi]) Sum[(6 (-1)^k)/(k \[Pi])

                Cos[(k \[Pi] x)/2] + (16 (-1)^k + 13)/(\[Pi] k) 
                Sin[(k \[Pi] x)/2],{k, 0, n}]

partialsums = Table[s[n, x], {n, 1, 5}];

f[x_] = Piecewise[{{-x^3-2x,-2 < x < 0},{-1+x,0<= x <= 2}}]

Plot[Evaluate[partialsums], {x, -4 Pi, 4 Pi}]

Any ideas of the best method to tackle something like this.

plotting fourier-analysis

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Plotting Partial Sums of Fourier Series