What is the peak resonance of convolving with a sine FIR filter?
If your signal was a windowed complex exponential, then the maximum of the magnitude of its discrete-time Fourier transform (DTFT) would equal the frequency of the complex exponential:

$$x[n]=\begin{cases}e^{jn\omega_0},\quad&amp;n\in[0,N-1]\\0,\quad&amp; \textrm{otherwise}\end{cases}\tag{1}$$

The DTFT of $(1)$ is easily computed from the convolution of the DTFT of a rectangular window $w[n]=1$ for $n\in[0,N-1]$ and zero otherwise, and the DTFT of $e^{jn\omega_0}$:

$$\textrm{DTFT}\{w[n]\}=W(e^{j\omega})=e^{-j(N-1)\omega/2}\frac{\sin\left(N\omega/2\right)}{\sin(\omega/2)}\tag{2}$$

$$\textrm{DTFT}\{e^{jn\omega_0}\}=2\pi\delta(\omega-\omega_0),\qquad |\omega|&lt;\pi,\quad |\omega_0|&lt;\pi\tag{3}$$

Note that the DTFT in $(3)$ is of course $2\pi$-periodic.

With $(2)$ and $(3)$ we can write the DTFT of $(1)$ as follows:

$$\begin{align}X(e^{j\omega})&amp;=W(e^{j\omega})\star\delta(\omega-\omega_0)\\&amp;=W\left(e^{j(\omega-\omega_0)}\right)\\&amp;=e^{-j(N-1)(\omega-\omega_0)/2}\frac{\sin\left(N(\omega-\omega_0)/2\right)}{\sin((\omega-\omega_0)/2)}\tag{4}\end{align}$$

The magnitude of $(4)$ clearly has a maximum at $\omega=\omega_0$ $(+2\pi k)$

However, for a windowed sinusoidal signal we get two contributions of the form $(2)$ centered at $\pm\omega_0$ because $\sin(n\omega_0)=(e^{jn\omega_0}-e^{-jn\omega_0})/2j$:

$$y[n]=\begin{cases}\sin(n\omega_0),\quad&amp;n\in[0,N-1]\\0,\quad&amp; \textrm{otherwise}\end{cases}\tag{5}$$

$$Y(e^{j\omega})=\frac{1}{2j}\left[e^{-j(N-1)(\omega-\omega_0)/2}\frac{\sin\left(N(\omega-\omega_0)/2\right)}{\sin((\omega-\omega_0)/2)}-\\\quad e^{-j(N-1)(\omega+\omega_0)/2}\frac{\sin\left(N(\omega+\omega_0)/2\right)}{\sin((\omega+\omega_0)/2)}\right]\tag{6}$$

I don't think that there is an analytical formula for the location of the maximum of the magnitude of $(6)$, but it is clear that due to the combination of the two terms in $(6)$, the maximum shifts away from $\omega_0$. That shift can become especially large for frequencies either close to DC or close to Nyquist. It is smallest for frequencies around half the Nyquist frequency (i.e., $f_s/4$). For small frequencies $\omega_0$, the actual frequency where the maximum occurs is smaller than $\omega_0$, whereas for large frequencies it is greater than $\omega_0$.