implementing a basic low pass Filter

I have a basic question. I want to implement a simple Low Pass 1 order filter with cut off frequency = 100Hz. Then I want to use this filter on a time domain signal of 1 Hz. I am expecting the output to be same as the input. But, When I convolve the impulse response of the filter with this input signal, I am getting an unwanted gain . I have attached my code. Can you help me to do this .

FS = 1000;

T = (1/FS);

fc = 100;

r = 10 * 1000;

c = 1 / ( 2 * pi * r * fc) ;

num = [(1/(r*c))];

den = [1 (1/(r*c))];

sys_tf_model = tf(num,den);

time = (0:T:10);

signal = sin ( 2 * pi * 1 * time);

impulse_response = impulse(sys_tf_model,time);

output1 = T * conv(signal,impulse_response);

output2 = lsim(sys_tf_model,signal,time) ;

subplot(3,1,1);plot(time,output1(1:1:length(time)));title('Convolution');

subplot(3,1,2);plot(time,output2);title('Lsim output');

subplot(3,1,3);plot(time,signal);title('Input');

[Sudarshan Kolar]

You’re approximating a continuous integral by a discrete sum. This introduces loss.

Replace the sampling period T by T/10 and you will see that the gap is reduced.

I would not recommend conv for your application.