  Oscillating neutron stars are sources of continuous gravitational waves. We
study analytically the excitation of stellar oscillations by the mechanical
impact on the stellar surface of ''clumps'' of stochastically accreted matter.
We calculate the waveform and spectrum of the gravitational wave signal emitted
by the accretion-driven pulsations. Results are generated for an idealised
model of a nonrotating, unmagnetised, one-component star with uniform
polytropic index $n_{\rm poly}$ assuming Newtonian gravity and the Cowling
approximation. We find that the excited mode amplitudes grow with increasing
$n_{\rm poly}$ and mode order $n$. The gravitational wave signal forms a
sequence of amplitude-modulated packets for $n_{\rm poly}=1$, lasting $\sim
10^{-3}$s after each impact. The gravitational wave strain increases with
increasing $n_{\rm poly}$, but decreases with increasing $n$ and increasing
multipole order $l$ for $n_{\rm poly}=1$. In the observing band of current
long-baseline interferometers, $g$-modes emit higher, narrower peaks in the
amplitude spectral density than $f$- and $p$-modes, with the highest peaks
reaching $\sim 10^{-26}$Hz$^{-1/2}$ for modes with damping time $\tau_{nl} \sim
10^{8}$yr. The root-mean-square strain $h_{\text{rms}}$, calculated by summing
over modes with $2\leq l\leq4$ and $\tau_{nl} \leq 10^{8}$yr, spans the range
$10^{-33} \leq h_{\text{rms}} \leq 10^{-32}$ for $1\leq n_{\text{poly}}\leq 2$.
