# Solutions HW #5 PHYS 160 Fall # Travis Hoppe restart: with(plots): signal := (N1,N2,t) -> sum(term(2*k-1,t),k=N1..N2); term := (n,t) -> a(n)*sin(2*Pi*n*t/TP); a := (n) -> 4/(Pi*n); TP := 1.125:

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plot( signal(1,50,t), t=0..2*TP, title="Two full cycles of the signal");

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filter := (n) -> (1+exp(n-9))**(-1); filtered_signal := (N1,N2,t) -> sum(term(2*k-1,t)*filter(2*k-1),k=N1..N2);

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plot( filtered_signal(1,15,t), t=0..TP, title="One full cycle of the filtered signal");

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

slope := (t) -> diff( filtered_signal(1,15,t), t); slope(t);

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUklZGlmZkclKnByb3RlY3RlZEc2JC1JMGZpbHRlcmVkX3NpZ25hbEdGJTYlIiIiIiM6OSRGMkYlRiVGJQ==

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

plot( slope(t), t=0..TP, title="Slope of filtered_signal" );

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

# Zeros of the slopes == maxima and minima of the orginal function Z := seq(fsolve( slope(t)=0, t=x ),x=0..TP/2, 0.01): Z := [seq(x, x in {Z})];

Ny0kISt0RCkqXDchIzUkIitXbTJdaSEjNiQiK3REKSpcN0YlJCIrKCkqSF0oPUYlJCIrJDRmKipcI0YlJCIrXytdN0dGJSQiKy40L0RKRiUkIistKygqXFBGJSQiK0B1LHZWRiUkIitNQioqKipcRiUkIisqM2ZcNylGJQ==

# Plug these values back into the orginal function Y_Z := [seq(filtered_signal(1,15,t), t in Z)];

Ny0kISsiSEpbYiohIzUkIitveVVTNiEiKiQiKyJISltiKkYlJCIrPGQtOTVGKCQiK2kpUl8nKipGJSQiK3c+PnkqKkYlJCIrZClSXycqKkYlJCIrPWQtOTVGKCQiKyNISltiKkYlJCIrbnlVUzZGKCQhK2UpUl8nKipGJQ==

# Visually, I like to see the solutions mapped back onto the orginal function (as a check!) P_Z := [seq( [Z[i],Y_Z[i]], i=1..nops(Z) )]: P1 := plot( filtered_signal(1,15,t), t=0..TP/2 ): P2 := plot( P_Z,t=0..TP/2,style=point,symbolsize=20,symbol="circle" ): display([P1,P2]);

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ZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2IlEhNiItJSVGT05URzYlJShERUZBVUxURyUoREVGQVVMVEciIzUlK0hPUklaT05UQUxHJStIT1JJWk9OVEFMRy0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJGcmISIiLSUpQk9VTkRTX1lHNiMkIiQrIiEiIi0lLUJPVU5EU19XSURUSEc2IyQiJSFSJCEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiVdUSEiIi0lKUNISUxEUkVORzYi

# The second half of the period is clearly a reflection of the first TP/2, thus the solution can be mapped back onto itself if one desired the other zeros.