# Why is the bandwidth doubled with AM?

Let's say I have an arbitrary signal which has the following frequency spectrum and a bandwidth of BNF:

Now I use Amplitude Modulation to transport the signal. The frequency spectrum will change accordingly:

Now I know that the required bandwidth doubles. I don't understand where the doubled bandwidth applies as I can't transport negative frequencies.

• You can't transport only the positive signal either, as it is a modulated complex phaser. Only by mixing the positive and negative frequencies do the imaginary components cancel, leaving you with a strictly real signal, which one can transport in the real world using a single analog channel. – hotpaw2 Jan 1 '17 at 9:22

What you've observed is just the difference between baseband modulation (your original plot) and carrier modulation (the second plot). Note that for the AM case, since the signal that modulates the carrier is real, the resulting carrier-modulated signal is symmetric. This means that you can get away with only transmitting one of the sidebands. This approach is called single sideband (SSB) modulation. With an SSB system, the carrier-modulated signal only has the bandwidth of approximately one of the sidebands of the original baseband signal.

Bandwidth is defined at positive frequencies. So for the lowpass (baseband) signal in your first figure, the bandwidth equals its upper cut-off frequency, whereas in the bandpass case (your second figure), the bandwidth equals the upper cut-off frequency minus the lower cut-off frequency. So, as you've correctly observed, the bandpass signal's bandwidth is twice the bandwidth of the baseband signal.

It's a misunderstanding that you "can't transport negative frequencies". You always do, as long as you send real-valued signals. Real-valued signals always have a (conjugate) symmetric spectrum.

It's true that this type of amplitude modulation (double-sideband AM) with twice the bandwidth of the baseband signal is inefficient. There are two options to avoid this inefficient use of bandwidth. First, use single sideband modulation (as mentioned in Jason R's answer), or, second, use a complex baseband signal, i.e., use two signals and orthogonal carriers. This is called quadrature modulation, and it uses the same bandwidth as conventional (double-sideband) amplitude modulation, but it transmits two signals instead of one.