# How transmission speed and bandwidth are linked?

I don't understand why if I have a larger bandwidth I can transmit data faster. Is this linked with this property of fourier transform?

thanks.

• Yes it is linked to the Fourier Transform. The shorter the pulse the greater the bandwidth – user28715 May 4 '19 at 21:36

Actually you also have to consider the noise floor of the communication channel and transmitted signal power to define the limit of data rate through an AWGN channel. The information capacity $$C$$ (bps) of the channel is given by the Shannon's formula:

$$C = B \cdot \log_2( 1 + \frac{ \sigma_x^2}{ \sigma_n^2 } )$$

where $$B$$ is the channel bandwidth in Hz., and $$\frac{ \sigma_x^2}{ \sigma_n^2 }$$ is the channel SNR (Signal to Noise Power Ratio).

One ideal case happens when there's no noise, then the capacity goes to infinity. This means that on a noiseless (ideal) channel you would transmit all the information (and more) instantly.

At larger channel bandwidth you can transmit signals with larger bandwidth, which is equivalent to shorter signal duration. This means you can transmit more signals for a given period of time for larger channel bandwidth.

Another way to look at it is in the limit, where the channel capacity is directly proportional to the bandwidth as in Shannon formula

$$C = W\log_2(1+\texttt{SNR})$$

where

$$C$$: the channel capacity in bps

$$W$$: is the channel bandwidth in Hz

$$\texttt{SNR}$$: the signal-to-noise ratio

Think of bandwidth of the width of a channel/tunnel. If it is wider you can send more data as compared to a narrow one. It is a simplified answer.