  Temporal difference (TD) learning is an important approach in reinforcement
learning, as it combines ideas from dynamic programming and Monte Carlo methods
in a way that allows for online and incremental model-free learning. A key idea
of TD learning is that it is learning predictive knowledge about the
environment in the form of value functions, from which it can derive its
behavior to address long-term sequential decision making problems. The agent's
horizon of interest, that is, how immediate or long-term a TD learning agent
predicts into the future, is adjusted through a discount rate parameter. In
this paper, we introduce an alternative view on the discount rate, with insight
from digital signal processing, to include complex-valued discounting. Our
results show that setting the discount rate to appropriately chosen complex
numbers allows for online and incremental estimation of the Discrete Fourier
Transform (DFT) of a signal of interest with TD learning. We thereby extend the
types of knowledge representable by value functions, which we show are
particularly useful for identifying periodic effects in the reward sequence.
