# What is meant by LFM (Linear Frequency Modulation) waveform?

I m a newbie in radar experiment on which currently i m working, and I m trying to understand the transmitted waveform which is LFM (Linear Frequency Modulation), but unable to interlink between the following parameters of transmitted signal waveform ,can someone explain to me how do these are connected to LFM?

Center frequency : 150kHz Sampling Frequency: 4000kHz Bandwidth : 50kHz Pulse length : 500microseonds

An LFM pulse is one in which the "instantaneous frequency" changes linearly over the duration of the pulse. By "instantaneous frequency" I mean the rate of change of phase. Over its $\tau=500\mu s$ duration, a pulse with "bandwidth" $B=50 kHz$ and center frequency $f_c=150 kHz$ would be defined by

$f(t)=A\cos(\theta(t))=A\cos(2\pi(f_c-B/2)t+\pi(B/\tau)t^2+\theta_0)$

Taking the derivative of phase with respect to time, we have

$\partial\theta(t)/\partial{t}=2\pi(f_c-B/2)+2\pi(B/\tau)t$

We can see that this sweeps from $2\pi(f_c-B/2)$ to $2\pi(f_c+B/2)$ over the duration of the pulse.

An LFM pulse provides better range resolution than an unmodulated pulse of the same duration.

• You need lots of $2\pi$'s in your equations. Else, you are discussing radian frequency and not Hertzian frequency. – Dilip Sarwate Apr 19 '18 at 15:57
• Thanks, Dilip Sarwate, you are right. I corrected this. – Ill-Conditioned Matrix Apr 19 '18 at 19:05