restart:with(plots):alias(u=Heaviside):assume(a>0);assume(b,real):with(inttrans):LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= We assume that a>0 and b is real Study of f(t) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=f:=t->cos(b*t)*exp(-a*t^2);F:=omega->fourier(f(t),t,omega):'F(omega)'=F(omega);

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSRjb3NHRiU2IyomSSJiR0YlIiIiOSRGL0YvLUkkZXhwR0YlNiMsJComSSJhR0YlRi9GMCIiIyEiIkYvRiVGJUYl

Ly1JIkZHNiI2I0kmb21lZ2FHRiUqKkkjYXxpckdGJSMhIiIiIiNJI1BpRyUqcHJvdGVjdGVkRyMiIiJGLC1JJWNvc2hHNiRGLkkoX3N5c2xpYkdGJTYjLCQqKEYpRitGJ0YwSSNifGlyR0YlRjBGL0YwLUkkZXhwR0YzNiMsJComLCYqJEY4RixGMCokRidGLEYwRjBGKUYrI0YrIiIlRjA=

f(t) behaviour with a = 1 , 2 , 3 , 4 , 5 and b = 10 distab=array[]:b:=10:for i from 1 to 5 do a:=i;distab[i]:=plot(f(x),x=3..-3,color=RGB(i*0.1, i*0.2, i*0.3),thickness=1);end: display(distab[1],distab[2],distab[3],distab[4],distab[5]);

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The darker curve is a=1 , the lighter curve is a=5. We can clearly see that if a is big, the amplitude of f(t) gets lower and vice versa. The period always stays unchanged. f(t) : behaviour with b = 1 , 2 , 3 , 4 , 5 and a = 1 distab=array[]:a:=1:for i from 1 to 5 do b:=i;distab[i]:=plot(f(x),x=3..-3,color=RGB(i*0.1, i*0.2, i*0.3),thickness=1);end: display(distab[1],distab[2],distab[3],distab[4],distab[5]);

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The darker curve is b=1 , the lighter curve is b=5. We can clearly see that if b is big, the period of f(t) gets lower but the amplitude is higher; and vice versa. Study of F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJm9tZWdhO0YnLyUlc2l6ZUdRIzIwRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUqdW5kZXJsaW5lR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVs1MSwxNTMsMTAyXUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==) F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJm9tZWdhO0YnLyUlc2l6ZUdRIzIwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==) : behaviour with a = 1 , 10 , 30 , 60 , 90 , 120 and b = 1 taba:=array([1,10,30,60,90,120]):b:=1: for i from 1 to 6 do a:=taba[i]: tab[i]:=plot(F(omega),omega=40..-40,color=RGB(i*0.1, i*0.2, i*0.3),thickness=1): end:display(tab[1],tab[2],tab[3],tab[4],tab[5],tab[6]);

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The darker curve is a=1 , the lighter curve is a=120. We can clearly see that if b is big, the period of F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEoJm9tZWdhO0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==) gets higher but the amplitude is lower; and vice versa. F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJm9tZWdhO0YnLyUlc2l6ZUdRIzIwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==) : behaviour with b = 1 , 10 , 20 , 30 , 70 , 100 and a = 1 tabb:=array([1,10,20,30,70,100]):b:=1: for i from 1 to 6 do b:=tabb[i]: tab[i]:=plot(F(omega),omega=180..-180,color=RGB(i*0.1, i*0.2, i*0.3),thickness=1):end:display(tab[1],tab[2],tab[3],tab[4],tab[5],tab[6]);

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The darker curve is b=1 , the lighter curve is b=120. We can clearly see that if b is big, the offset of F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEoJm9tZWdhO0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==) from zero gets higher ; and vice versa. At a certain stage, we observe that the amplitude stays the same (about b=25). Comparison of f(t) and F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJm9tZWdhO0YnLyUlc2l6ZUdRIzIwRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUqdW5kZXJsaW5lR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVs1MSwxNTMsMTAyXUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==) F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KVEoJm9tZWdhO0YnLyUlc2l6ZUdRIzIwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2ZvcmVncm91bmRHUSxbMTUzLDIwNCwwXUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y6) and f(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KVEidEYnLyUlc2l6ZUdRIzIwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y0LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJ0YvRjJGNUY3RjpGPQ==) with a=1 and b=4 for bothJSFH a:=1:b:=4:display(plot(f(t),color=BLUE),plot(F(omega),omega=30..-30,color=GREEN));

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At Special cases of f(t) and F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJm9tZWdhO0YnLyUlc2l6ZUdRIzIwRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUqdW5kZXJsaW5lR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVs1MSwxNTMsMTAyXUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==) F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KVEoJm9tZWdhO0YnLyUlc2l6ZUdRIzIwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2ZvcmVncm91bmRHUSxbMTUzLDIwNCwwXUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y6) and f(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KVEidEYnLyUlc2l6ZUdRIzIwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y0LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJ0YvRjJGNUY3RjpGPQ==) with a=0 and b=1 for bothLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= a:=0:b:=1:display(plot(f(t),color=BLUE),plot(F(omega),omega=30..-30,color=GREEN));

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We can clearly see that when a is naught, the F(LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJm9tZWdhO0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUqdW5kZXJsaW5lR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==) curve isn't workable since we have 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 f(t+2) a=1 and b=1 restart:with(plots):alias(u=Heaviside):assume(a>0);assume(b,real):with(inttrans):LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=f:=t->cos(b*t)*exp(-a*t^2);F:=omega->fourier(f(t),t,omega):'F(omega)'=F(omega);a:=1:b:=1:

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSRjb3NHRiU2IyomSSJiR0YlIiIiOSRGL0YvLUkkZXhwR0YlNiMsJComSSJhR0YlRi9GMCIiIyEiIkYvRiVGJUYl

Ly1JIkZHNiI2I0kmb21lZ2FHRiUqKkkjYXxpckdGJSMhIiIiIiNJI1BpRyUqcHJvdGVjdGVkRyMiIiJGLC1JJWNvc2hHNiRGLkkoX3N5c2xpYkdGJTYjLCQqKEYpRitGJ0YwSSNifGlyR0YlRjBGL0YwLUkkZXhwR0YzNiMsJComLCYqJEY4RixGMCokRidGLEYwRjBGKUYrI0YrIiIlRjA=

'f(t+2)'=f(t+2);plot(f(t+2),t=-5..1);

Ly1JImZHNiI2IywmSSJ0R0YlIiIiIiIjRikqJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYmRiktSSRleHBHRi42IywkKiRGJ0YqISIiRik=

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

F:=omega->fourier(f(t+2),t,omega):'F(omega)'=F(omega);LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Ly1JIkZHNiI2I0kmb21lZ2FHRiUqKEkjUGlHJSpwcm90ZWN0ZWRHIyIiIiIiIy1JJWNvc2hHNiRGKkkoX3N5c2xpYkdGJTYjLCRGJ0YrRiwtSSRleHBHRjA2IywmIyEiIiIiJUYsKiZGJ0YsLCZGJ0Y5XiMiIilGLEYsI0YsRjpGLA==

plot(F(omega),omega=30..-30);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

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

f(5t) a=1 and b=1 'f(5*t)'=f(5*t);plot(f(5*t),t=-1..1);

Ly1JImZHNiI2IywkSSJ0R0YlIiImKiYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGJiIiIi1JJGV4cEdGLTYjLCQqJEYoIiIjISNERjA=

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

F:=omega->fourier(f(5*t),t,omega):'F(omega)'=F(omega);LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Ly1JIkZHNiI2I0kmb21lZ2FHRiUsJCooSSNQaUclKnByb3RlY3RlZEcjIiIiIiIjLUklY29zaEc2JEYrSShfc3lzbGliR0YlNiMsJEYnI0YtIiM1Ri0tSSRleHBHRjE2IywmIyEiIiIiJUYtKiRGJ0YuI0Y8IiQrIkYtI0YtIiIm

plot(F(omega),omega=-50..50);

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

f(4t+3) a=1 and b=1 'f(4*t+3)'=f(4*t+3);plot(f(4*t+3),t=-2..1);

Ly1JImZHNiI2IywmSSJ0R0YlIiIlIiIkIiIiKiYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGJkYrLUkkZXhwR0YvNiMsJCokRiciIiMhIiJGKw==

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

F:=omega->fourier(f(4*t+3),t,omega):'F(omega)'=F(omega);LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Ly1JIkZHNiI2I0kmb21lZ2FHRiUsJCooSSNQaUclKnByb3RlY3RlZEcjIiIiIiIjLUklY29zaEc2JEYrSShfc3lzbGliR0YlNiMsJEYnI0YtIiIpRi0tSSRleHBHRjE2IywmIyEiIiIiJUYtKiZGJ0YtLCZGJ0Y8XiMiI1tGLUYtI0YtIiNrRi0jRi1GPQ==

plot(F(omega),omega=-30..30);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

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

JSFH