  Recently, simple metrics of spherically symmetric black hole in dark matter
halo were obtained by Xu et al, and extended to the case of rotation. Based on
these two metrics of spherically symmetric black hole, we study the echo
signals of CDM and SFDM models in scalar and electromagnetic fields, and make
comparisons with the Schwarzschild black hole. Our results show that the black
hole echoes in dark matter halo are different from the Schwarzschild black
hole, hence the signals of echo can be used to distinguish different dark
matter models. The echo signals appear after the first exponential decay, and
decrease with increasing parameter $l$. The values of echo of CDM are
approximately between $10^{-1}$ and $10^{-5}$, that of SFDM are between
$10^{-2}$ and $10^{-6}$; The values of classic black hole are approximately
between $10^{-4}$ and $10^{-8}$. The overall echoes of CDM are stronger than
that of SFDM in the same condition, which is easier to be detected. In
addition, the values of echo frequency using the six-order WKB method and Prony
method are in good agreement.
