fs$=103\mathrm{.}4$e$3$;

Ts$=1/$fs;

tlen$=\mathrm{.}4$;

t$=0$:Ts:tlen$-$Ts;

N$=$length$($t$)$;

x$=$sin$(2*$pi$*$f$1*$t$)$;

standev$=1$;

noise$=$randn$(1,$N$)*$standev;

xn$=$x$+$noise;

Omegacf$=0\mathrm{.}004797*$pi;

Omegao$=0\mathrm{.}02418*$pi;

M$=1001$;

n$=(0$:M$-1)-$floor$($M$/2)$;

h$=$Omegacf$/$pi$*$sinc$($n$*$Omegacf$/$pi$)$;

w$=$hamming$($M$)\text{'}$;

A$=1$;

B$=$h$.*$w$.*$cos$($n$*$Omegao$)$;

y$=$filter$($B$,$A$,$xn$)$;

subplot$(2,1,1)$

plot$($t$,$x$,$'LineWidth',$3)$;

hold on

plot$($t$,$xn$,$'LineWidth',$1)$;

plot$($t$,$y$,\text{'}$g$\text{'},$'LineWidth',$2)$;

axis$([1/$f$1*1001/$f$1*110-44])$;

xlabel$(\text{'}$time$,$s$\text{'})$;

ylabel$(\text{'}$amplitude$,$ arbitrary units'$)$;

legend$(\text{'}$original signal','with noise','filtered'$)$;

hold off

X$=$fft$($x$)$;

Xn$=$fft$($xn$)$;

Y$=$fft$($y$)$;

subplot$(2,1,2)$

fbin$=$fs$/$N;

f$=0$:fbin:fs$-$fbin;

plot$($f$,20*$log$10($abs$($X$)),$'LineWidth',$3)$;

hold on

plot$($f$,20*$log$10($abs$($Xn$)),$'LineWidth',$1)$;

plot$($f$,20*$log$10($abs$($Y$)),\text{'}$g$\text{'},$'LineWidth',$2)$;

xlabel$(\text{'}$frequency$,$ Hz$\text{'})$;

ylabel$(\text{'}$magnitude response, dB$\text{'})$;

legend$(\text{'}$noisy signal spectrum','filtered spectrum'$)$

axis$([1$e$2$ fs$/2-40100])$

hold off

What band of frequencies will this filter keep?