The instantaneous frequency of a sine wave can be estimated using a Hilbert transformer. However, there is a ripple in the amplitude characteristics of finite-order Hilbert transformers. The estimate thus contains an oscillatory component that depends on this ripple. In this paper, we theoretically show that the frequency of the oscillation component is an even multiple of the input signal frequency. We propose a method for designing a low-pass FIR filter with variable transmission zeros. A simulation is used to show that this filter improves estimation accuracy.