diff --git a/base/fft/ctfft.jl b/base/fft/ctfft.jl
index e94babf8f8f13..8965ffb67e4db 100644
--- a/base/fft/ctfft.jl
+++ b/base/fft/ctfft.jl
@@ -103,9 +103,9 @@ function CTPlan{Tr<:FloatingPoint}(::Type{Complex{Tr}}, forward::Bool, n::Int)
 end
 
 plan_fft{Tr<:FloatingPoint}(x::AbstractVector{Complex{Tr}}) =
-    CTPlan(Complex{Tr}, true, length(x))
+    CTPlan(Complex{Tr}, true, length(x))::CTPlan{Complex{Tr},true}
 plan_bfft{Tr<:FloatingPoint}(x::AbstractVector{Complex{Tr}}) =
-    CTPlan(Complex{Tr}, false, length(x))
+    CTPlan(Complex{Tr}, false, length(x))::CTPlan{Complex{Tr},false}
 
 function applystep{T}(p::CTPlan{T},
                       x::AbstractArray{T}, x0, xs,
diff --git a/base/fft/fftn.jl b/base/fft/fftn.jl
index c9883cc045f6f..fa7dc726c51bf 100644
--- a/base/fft/fftn.jl
+++ b/base/fft/fftn.jl
@@ -49,9 +49,9 @@ function MultiDimPlan{T<:Complex}(::Type{T}, forward::Bool, region, sz)
 end
 
 plan_fft{Tr<:FloatingPoint}(x::AbstractArray{Complex{Tr}}, region) =
-    MultiDimPlan(Complex{Tr}, true, region, size(x))
+    MultiDimPlan(Complex{Tr}, true, region, size(x))::MultiDimPlan{Complex{Tr}, true}
 plan_bfft{Tr<:FloatingPoint}(x::AbstractArray{Complex{Tr}}, region) =
-    MultiDimPlan(Complex{Tr}, false, region, size(x))
+    MultiDimPlan(Complex{Tr}, false, region, size(x))::MultiDimPlan{Complex{Tr}, false}
 
 # recursive execution of a MultiDim plan, starting at dimension d, for
 # strided arrays (so that we can use linear indexing):
diff --git a/test/fft.jl b/test/fft.jl
index 857ff801d05a8..9f9f6b07f7d41 100644
--- a/test/fft.jl
+++ b/test/fft.jl
@@ -356,3 +356,18 @@ for T in (Complex128, Complex{BigFloat})
         end
     end
 end
+
+# issue #9772
+for x in (randn(10),randn(10,12))
+    z = complex(x)
+    y = rfft(x)
+    @inferred rfft(x)
+    @inferred brfft(x,18)
+    @inferred brfft(y,10)
+    for f in (fft,plan_fft,bfft,plan_bfft,fft_)
+        @inferred f(x)
+        @inferred f(z)
+    end
+    # note: inference doesn't work for plan_fft_ since the
+    #       algorithm steps are included in the CTPlan type
+end