# Solving equation with convolution

I have the measured signal $$y(t)$$ that can be modeled in the frequency domain as $$Y(f)$$:

$$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$

where $$\ast$$ is the convolution. I know $$A(f)$$, $$B(f)$$, and $$C(f)$$. I measure $$Y(f)$$. Is there a way to retrieve $$X(f)$$? I know that if $$C(f)$$ is constant and $$1$$, then I can easily retrieve $$X(f)$$ except for frequencies with $$A(f)=B(f)$$. But how do I go about this for an arbitrary but known $$C(f)$$?

• What's the order of operation? Is it $[X(f) \cdot B(f)]*C(f)$ or $X(f) \cdot [B(f)*C(f)]$ – Hilmar Oct 9 at 19:44
• I was about to ask the same question. What is the associativity? – Laurent Duval Oct 9 at 19:49
• First $X(f)B(f)$, then the convolution. – Test123 Oct 9 at 19:52